Midterm Examination 1 Solutions

Problem 1:

When you bounce a soccer ball off a stone wall, the ball

(A) retains essentially all of its momentum but transfers a great deal of energy to the wall. [6.2% picked]

(B) transfers a great deal of momentum and energy to the wall. [6.6% picked]

(C) retains essentially all of its energy but transfers a great deal of momentum to the wall. [76.5% picked]

(D) retains essentially all of its energy and momentum. [10.6% picked]

Answer: (C) retains essentially all of its energy but transfers a great deal of momentum to the wall. [76.5% picked]

Why: The ball pushes on the wall during the bounce, so it transfers momentum to the wall by way of an impulse (force * time). The wall doesn't move, however, so the ball cannot do work on the wall and transfers no energy to the wall.

Problem 2:

You jump while standing on a bathroom scale and the scale briefly reads more than your actual weight. During that moment, the scale is exerting an upward force on you that is

(A) equal to your weight and you are accelerating upward. [9.7% picked]

(B) greater than your weight and you are accelerating upward. [72.6% picked]

(C) greater than your weight and your velocity is constant. [14.2% picked]

(D) equal to your weight and your velocity is constant. [3.1% picked]

Answer: (B) greater than your weight and you are accelerating upward. [72.6% picked]

Why: The scale is accurately reporting that it is pushing upward on you with a force greater than your weight. You pushed extra hard on it and it is pushing extra hard back on you. Because its upward force on you is greater in amount than your downward weight, the net force you're experiencing is upward and you are accelerating upward.

Problem 3:

A boy is bicycling up a hill and appears to need some help. As he passes you, you reach out with your hand and exert an uphill force of 10 N on him. When you do this, the boy exerts

(A) a downhill force of somewhat more than 10 N on you, because, in addition to the reaction force, he must accelerate your hand downhill. [1.3% picked]

(B) no downhill force on you at all, because the force of his momentum is already enough to keep him moving uphill. [0.4% picked]

(C) a downhill force of 10 N on you, because forces always come in equal but oppositely directed pairs. [95.6% picked]

(D) a downhill force of somewhat less than 10 N on you, because his uphill velocity reduces the force he needs to accelerate uphill. [2.2% picked]

Answer: (C) a downhill force of 10 N on you, because forces always come in equal but oppositely directed pairs. [95.6% picked]

Why: In accordance with Newton's third law, the boy pushes back on you with a force that is equal in amount but opposite in direction to the force you exert on the boy. The fact that the boy is bicycling up the hill makes no difference at all.

Problem 4:

You are moving into a loft apartment and are now dragging an old carpet across the floor in a straight line at a steady speed. Which of the following statements about the forces acting on the carpet is correct?

(A) If you were to exert twice as much force on the carpet, it would slide across the floor twice as fast. [14.2% picked]

(B) The amount of force that you're exerting on the carpet must be equal to amount of force that friction is exerting on it. [40.7% picked]

(C) The amount of force that you're exerting on the carpet must be more than the amount of its weight. [1.8% picked]

(D) The amount of force that you're exerting on the carpet must be more than the amount of force that friction is exerting on it. [41.6% picked]

Answer: (B) The amount of force that you're exerting on the carpet must be equal to amount of force that friction is exerting on it. [40.7% picked]

Why: The carpet is coasting across the floor at constant velocity, so it is not accelerating and the net force it is experiencing is zero. Therefore, the forward force you exert on the carpet must exactly balance the backward sliding friction force that the floor is exerting on the carpet.

Problem 5:

A sack of flour will bounce higher when you drop it onto a mattress than when you drop it onto a cement floor. That's because

(A) the sack of flour has more momentum when it hits the mattress than when it hits the cement floor. [3.1% picked]

(B) the cement floor has more mass than the mattress. [0.4% picked]

(C) the cement floor exerts less torque on the sack of flour than the mattress does. [2.7% picked]

(D) the mattress deforms more as it slows the falling sack of flour and it stores more of the collision energy. [93.8% picked]

Answer: (D) the mattress deforms more as it slows the falling sack of flour and it stores more of the collision energy. [93.8% picked]

Why: The mattress is acting as a trampoline for the sack of flour. Although the sack itself has a very small coefficient of restitution (it stores and returns very little of the collision energy invested in it), the mattress is relativley lively. By letting the sack bounce on a soft, elastic surface, you are allowing the mattress to store and return a substantial fraction of the collision energy as rebound energy. The sack bounces much higher as a result.

Problem 6:

On a recent trip to the moon, you decide to measure your weight and mass. You find that

(A) your mass is still essentially unchanged but your weight is less than on earth. [95.6% picked]

(B) your weight is still essentially unchanged but your mass is less than on earth. [2.2% picked]

(C) your weight and mass have both changed significantly. [0.4% picked]

(D) neither your weight nor your mass have changed much. [1.8% picked]

Answer: (A) your mass is still essentially unchanged but your weight is less than on earth. [95.6% picked]

Why: Your mass is unaffected by changes of venue because it is the measure of your inertia. Your weight, however, depends on the local strength of gravity and changes with venue.

Problem 7:

You're trying to win a stuffed animal at the fair by knocking over a stack of heavy milk bottles with a projectile. You have a choice of four projectiles: a 1-kilogram beanbag, a 2-kilogram beanbag, a 1-kilogram bouncy ball, and a 2-kilogram bouncy ball. Assuming that you can throw each of these projectiles at the same final speed, which one will be most effective at knocking over the milk bottles?

(A) The 2-kilogram beanbag. [10.6% picked]

(B) The 1-kilogram bouncy ball. [1.3% picked]

(C) The 1-kilogram beanbag. [1.8% picked]

(D) The 2-kilogram bouncy ball. [85.8% picked]

Answer: (D) The 2-kilogram bouncy ball. [85.8% picked]

Why: The more massive the projectile, the momentum it carries for a given velocity. A bouncy projectile transfers more than all of its forward momentum to the milk bottles because it not only comes to a stop, it actually bounces backward. Overall, the 2-kg bouncy ball starts with lots of momentum in the forward direction and ends up with lots of momentum in the backward direction (it ends up with a deficit of forward momentum). The missing forward momentum has been transferred to the milk bottles, so they are likely to tip over.

Problem 8:

You are bicycling along a quiet street when a child runs in front of you to retrieve a toy. You slam on the brakes and lock your wheels. The bicycle skids to a stop. What has become of your kinetic energy?

(A) It's now thermal energy in the wheels and ground. [94.7% picked]

(B) It's still present in you, as it must be because kinetic energy is conserved and can't be created or destroyed. [1.8% picked]

(C) It's now elastic potential energy in the brakes. [0.9% picked]

(D) It's now gravitational potential energy in the wheels. [2.2% picked]

Answer: (A) It's now thermal energy in the wheels and ground. [94.7% picked]

Why: When your bicycle skids to a stop on the pavement, frictional forces appear between the wheels and the ground. The ground exerts a backward frictional force on each wheel and each wheel exerts a forward frictional force on the ground. Since the ground doesn't move, the forward frictional forces do zero work on the ground. But the wheels move forward during the stopping process, so the backward frictional force that the ground exerts on those wheels does negative work on the wheels. It appears that work (energy) has disappeared. However, that missing work has become thermal energy in the wheels and the ground, which are both somewhat warmer than they were before you stopped.

Problem 9:

You are building a decorative mobile, a sculpture consisting of kitchen utensils that hang from one another on strings. One long metal fork is supported by a single string. For the fork to be balanced, that supporting string must be placed

(A) at the fork's center of mass. [53.5% picked]

(B) midway between the two ends of the fork. [0.0% picked]

(C) at the fork's center of percussion. [0.0% picked]

(D) at the fork's center of gravity. [46.0% picked]

Answer: (D) at the fork's center of gravity. [46.0% picked]

Why: Balancing a hanging fork so that it doesn't tip heavy-side down is a weight problem. You need to support the fork at its center of gravity (its center of weight). Since the fork's weight then acts at the support point, it produces no torque on the fork about its support point and the fork is balanced. The fork's center of mass happens to coincide with its center of gravity, but center of mass is about inertia (you might call it the fork's center of inertia) and that's not what matters here.

Problem 10:

While wandering in the dark toward the refrigerator, you accidentally walk into a concrete wall and come to a sudden stop without bouncing back. Fortunately, that wall was covered with a soft fabric wall hanging. Coming to a stop on the soft fabric was more pleasant than coming to a stop on the concrete because you transfer

(A) the same momentum to either surface, but you transfer it more slowly to the fabric than to the concrete. [95.6% picked]

(B) more momentum to the concrete than to the fabric. [2.2% picked]

(C) more energy to the concrete than to the fabric. [1.3% picked]

(D) more velocity to the concrete than to the fabric. [0.9% picked]

Answer: (A) the same momentum to either surface, but you transfer it more slowly to the fabric than to the concrete. [95.6% picked]

Why: Whether you come to a stop on the concrete or on the carpet, you transfer all of your forward momentum to the object you hit. In other words, the impulse (force * time) you do on the wall or carpet is the same. However, by stopping on the carpet, you transfer that momentum slowly with a small force. That same impulse done on the concrete wall would involve a large force over a small time.

Problem 11:

You toss a basketball straight up. Disregarding any effects of due to the air, what force or forces are acting on the basketball while it is above your hands?

(A) Its weight. [68.6% picked]

(B) Its weight along with a steadily decreasing upward force. [2.7% picked]

(C) A steadily decreasing upward force from the moment it leaves your hands until it reaches its highest point and then a steadily increasing downward force as the basketball returns toward your hands. [13.3% picked]

(D) Its weight along with an upward force that steadily decreases until the basketball reaches its highest point. After that point, there is only the constant downward force of gravity. [14.6% picked]

Answer: (A) Its weight. [68.6% picked]

Why: Once the basketball is out of your hands, the only force acting on it is its weight. It continues upward because of inertia alone. It is actually accelerating downward the entire time.

Problem 12:

You are working in a pizza parlor and have learned how to toss and spin the dough to form large disks. You find that the larger each disk becomes as you spin it, the harder it is to stop the disk from spinning. This effect occurs because spreading the dough into a larger disk increases its

(A) angular velocity. [18.6% picked]

(B) weight. [0.4% picked]

(C) rotational mass. [80.1% picked]

(D) mass. [0.0% picked]

Answer: (C) rotational mass. [80.1% picked]

Why: As the pizza disk becomes larger, its rotational mass increases. The farther its portions of mass are from its center of mass, the more those portions contributes to its rotational inertia, as measured by its rotational mass.

Problem 13:

You are riding the subway and there is a team of roller skaters standing in aisle. The skaters are not holding on to anything as the subway travels along its route. Suddenly, the roller skaters begin rolling toward the right side of the subway car. You know that the subway car

(A) has accelerated toward the left. [92.0% picked]

(B) has accelerated toward the right. [2.7% picked]

(C) is moving at constant velocity toward the left. [4.0% picked]

(D) is moving at constant velocity toward the right. [0.4% picked]

Answer: (A) has accelerated toward the left. [92.0% picked]

Why: The subway car is driving out from under the roller skaters. As the subway car turns left, it accelerates left. The skaters coast straight. As a result, the skaters move rightward relative to the subway car.

Problem 14:

You are riding a stand-up roller coaster and, at this moment, your body is oriented vertically as though you were standing on the ground. However, you feel extraordinarily heavy, as though the earth were pulling you directly downward several times more strongly than usual. At this moment,

(A) your velocity must be downward. [1.3% picked]

(B) your velocity must be upward. [4.0% picked]

(C) your acceleration must be upward. [84.5% picked]

(D) your acceleration must be downward. [10.2% picked]

Answer: (C) your acceleration must be upward. [84.5% picked]

Why: You are experiencing a feeling of acceleration in the downward direction. Since feelings of acceleration always point in the direction opposite you actual acceleration, you mujst be accelerating upward.

Problem 15:

A cheerleader leaps into the air with her arms and legs extended and then pulls herself into a compact ball to complete a somersault. She opens up again and lands on her feet. During the time that she is not touching the ground, one aspect of her motion that is constant is her

(A) angular momentum. [48.2% picked]

(B) velocity. [8.0% picked]

(C) angular velocity. [10.2% picked]

(D) momentum. [31.0% picked]

Answer: (A) angular momentum. [48.2% picked]

Why: While the cheerleader is in the air, she is experiencing a net force (due to her weight) but zero torque about her center of mass (her weight effectively acts at her center of gravity, which coincides with her center of mass). As a result, her momentum changes (she experiences an impulse due to gravity) but her angular momentum remains constant (she experiences no angular impulse).

Problem 16:

You are arm-wrestling with a friend. You are sitting across from one another with your right arms locked together and each of you is trying to twist the other's arm down to the tabletop. After a few minutes of struggling, you succeed in twisting your friends arm to the tabletop and win. As you won,

(A) you did no work on your friend and the torque that you exerted on your friend was equal in amount to the torque that your friend exerted on you. [1.3% picked]

(B) you did no work on your friend, but the torque that you exerted on your friend was greater in amount than the torque that your friend exerted on you. [4.9% picked]

(C) you did work on your friend and the torque that you exerted on your friend was greater in amount than the torque that your friend exerted on you. [33.2% picked]

(D) you did work on your friend, but the torque that you exerted on your friend was equal in amount to the torque that your friend exerted on you. [60.6% picked]

Answer: (D) you did work on your friend, but the torque that you exerted on your friend was equal in amount to the torque that your friend exerted on you. [60.6% picked]

Why: The torque you exert on your friend and the torque your friend exerts on you must be equal and opposite. They are a Newton's third law pair. However, each of those torques acts on a different object: your torque on your friend acts on your friend, while your friend's torque on you acts on you. You win because the torque your shoulder exerts on your arm in the winning direction is greater in amount than the torque your friend exerts on your arm in the losing direction. The net torque on your arm is thus in the winning direction and your arm undergoes angular acceleration in the winning direction.

Problem 17:

You are water-skiing behind your new yacht and the rope from the yacht is pulling you forward. At this moment, you are traveling in a straight line path at a constant speed. The net force you are experiencing is

(A) in the upward direction. [3.1% picked]

(B) in the forward direction. [5.8% picked]

(C) in the backward direction. [2.7% picked]

(D) zero. [88.1% picked]

Answer: (D) zero. [88.1% picked]

Why: Since you are traveling in a straight line path at a constant speed, your velocity is constant and you are not accelerating. Your acceleration is always proportional to the net force you are experiencing, so the net force your are experiencing is zero.

Problem 18:

You are watching children play a game of tug-o-war with a plastic clothesline. The two teams are pulling at opposite ends of the cord and each team is trying to drag the other team into a mud puddle that lies between them. After a few minutes without progress, the team on the right suddenly pulls hard toward the right. The team on the left has anticipated this threat and is able to keep their end of the rope from moving. The right end of the rope stretches toward the right and the rope breaks. Breaking the rope required energy and that energy was provided by

(A) the team on the right. [31.9% picked]

(B) neither team. It was instead provided by chemical potential energy in the rope itself. [4.9% picked]

(C) the team on the left. [4.0% picked]

(D) both teams. [58.0% picked]

Answer: (A) the team on the right. [31.9% picked]

Why: To transfer energy to the rope, a team must do work on that rope.The team on the right pulls the rope toward the right and the portion of rope in their hands moves toward the right, so they do work on that portion of rope. The team on the left pulls the rope toward the left, but that portion of rope does not move so they do no work on that portion of rope.

Problem 19:

You're having trouble loosening a rusty nut with a small wrench, so you borrow a large wrench from your neighbor. Exerting only a modest force on the handle of this new wrench easily unscrews the nut. The large wrench helps because it

(A) allows you to exert your force far from the center of rotation, so that you produce a large torque on the nut. [84.5% picked]

(B) has a large acceleration and a large mass, so the force it produces is large, according to the equation F=ma. [4.9% picked]

(C) has a large moment of inertia so that it develops a great deal of angular momentum when you exert a force on it. [3.5% picked]

(D) has a large mass so that its inertia allows you to overcome the nut's velocity and accelerate it around in a circle. [4.4% picked]

Answer: (A) allows you to exert your force far from the center of rotation, so that you produce a large torque on the nut. [84.5% picked]

Why: Loosening the nut requires that you exert a torque on the nut. Your goal is to exert a torque that is larger in amount than the frictional torque preventing the nut from starting to turning. You exert your torque by pulling on the handle of the wrench, at right angles to the lever arm provided by that wrench. Since the torque you produce is equal in amount to the lever arm times the force you exert at right angles to the lever arm, lengthening the lever arm allows you to produce more torque.

Problem 20:

An amazing skater is coasting past you on frictionless ice. You reach out and drop a bouquet of roses straight down into her open arms. As a result receiving your gift, the skater

(A) retains exactly the same forward velocity because velocity is conserved. [4.0% picked]

(B) slows down because her initial momentum is now distributed over more mass. [68.6% picked]

(C) retains exactly the same forward velocity because only her overall weight has increased. [22.6% picked]

(D) speeds up because her forward momentum has increased. [3.1% picked]

Answer: (B) slows down because her initial momentum is now distributed over more mass. [68.6% picked]

Why: The skater has the same total momentum before and after receiving the roses, but that momentum is distributed over more mass (the skater plus the roses). Since the skater's momentum is the product of her mass times her velocity, increasing her mass requires that her velocity decrease. In other words, she shares her original momentum with the roses and has to travel more slowly as a result.

Problem 21:

Two bowling balls, one of which weighs twice as much as the other, roll off of a horizontal table together at the same initial velocity. In this situation,

(A) both balls hit the floor at approximately the same time, but the heavier ball lands considerably farther from the table than the lighter ball does. [23.5% picked]

(B) the heavier ball hits the floor first and it lands considerably farther from the table than the lighter ball does. [0.9% picked]

(C) both balls hit the floor at approximately the same time and at the same distance from the table. [66.4% picked]

(D) the heavier ball hits the floor first and it lands considerably closer to the table than the lighter ball does. [9.3% picked]

Answer: (C) both balls hit the floor at approximately the same time and at the same distance from the table. [66.4% picked]

Why: The two balls coast horizontally while falling vertically. Since there is no horizontal force acting on either one, they travel steadily forward horizontally, side by side. Since they both fall with the same downward acceleration, they descend together, side-by-side. And overally, the travel exact the same arc and hit the floor at the same time and the same distance from the table.

Problem 22:

When you pull a tablecloth out from under a set of dishes, it's important to pull the cloth as fast as possible because

(A) the momentum transferred to the dishes is proportional to the time during which the cloth pulls on them. [39.8% picked]

(B) the force of sliding friction that the cloth exerts on the dishes is proportional to the time during which the cloth is moving. [37.2% picked]

(C) the weight of the dishes on the cloth is proportional to the time during which the cloth is moving. [2.7% picked]

(D) the work done on the dishes by the cloth is proportional to the time during which the cloth pulls on them. [19.0% picked]

Answer: (A) the momentum transferred to the dishes is proportional to the time during which the cloth pulls on them. [39.8% picked]

Why: When you pull the tablecloth, a sliding frictional force will act from the cloth on the dishes. The strength of a sliding frictional force is relatively independent of speed, so you can't change it by pulling faster or slower. You therefore can't change how much work that force does on the dishes, since work is force times distance and neither depends on speed. But you can change the amount of momentum that force transfers to the dishes. The faster you pull, the shorter the time over which sliding friction acts on the dishes and the less momentum it transfers to those dishes.

Problem 23:

You are at the gym, exercising on a step machine. You have one foot on each of the machine's pedals and you move those pedals up and down as you step. The pedals always push upward on your feet, but they push harder while moving downward than while moving upward. When during this exercise are you transferring energy to the step machine?

(A) As the pedals move downward. [62.4% picked]

(B) As the pedals move upward. [1.8% picked]

(C) As the pedals move either upward or down. [26.5% picked]

(D) When the pedals are accelerating. [8.0% picked]

Answer: (A) As the pedals move downward. [62.4% picked]

Why: Since you are pushing downward on the pedals, you do work on the pedals as they move downward but negative work on the pedals as they move upward. Since the question asks when you transfer energy to the step machine and we assume that that energy is positive, the only time you transfer energy to the step machine is when the pedals move downward.

Problem 24:

You are watching a volleyball game and the server has just hit the ball over the net toward the opponents side. Once the ball has left the server's hand and is heading forward toward the opponents' side, it experiences

(A) a forward horizontal force until it reaches its highest point over the net and then a backward horizontal force for the remainder of its trip. [2.2% picked]

(B) a forward horizontal force that remains constant all the way to the opponent's side. [5.8% picked]

(C) no horizontal force in the forward direction. [83.6% picked]

(D) a forward horizontal force that diminishes gradually as the ball approaches the opponents' side. [8.4% picked]

Answer: (C) no horizontal force in the forward direction. [83.6% picked]

Why: Neglecting forces due to the air itself, there is no horizontal force acting on the volleyball while it is in the air. It continues to move forward horizontally because of inertia.

Problem 25:

You are practicing the trapeze at circus camp and you lose your grip on the bar. You fall into the net far below and bounce comfortably up and down. After a few seconds, you settle down at equilibrium in the net. When during your fall and first rebound upward were you accelerating downward?

(A) Whenever you were above your equilibrium in the net. [51.8% picked]

(B) Only when you were not touching the net during both your fall and your rebound. [30.5% picked]

(C) Only until you touched the net during your initial fall. [7.1% picked]

(D) Only when you had not yet reached the lowest point during your first bounce off the net. [9.7% picked]

Answer: (A) Whenever you were above your equilibrium in the net. [51.8% picked]

Why: As long as the net force on you is downward, you accelerate downward. While you are in free fall, therefore, you accelerate downward. And when the net is pushing you upward too weakly to support your weight, you accelerate downward. It isn't until you dent the net so deeply that it exerts an upward force on you that is equal in amount to your weight that you finally experience zero net force and stop accelereating downward. At that point, you are at equilibrium.

Problem 26:

You are sitting on a merry-go-round at the playground and it is spinning rapidly. As the merry-go-round spins, the net force on you points

(A) away from the merry-go-round's center and you experience a feeling of acceleration toward its center. [7.5% picked]

(B) away from the merry-go-round's center and you experience a feeling of acceleration away from its center. [3.5% picked]

(C) toward the merry-go-round's center and you experience a feeling of acceleration toward its center. [7.5% picked]

(D) toward the merry-go-round's center and you experience a feeling of acceleration away from its center. [80.5% picked]

Answer: (D) toward the merry-go-round's center and you experience a feeling of acceleration away from its center. [80.5% picked]

Why: While you are traveling in a circle at constant speed, you are accelerating directly toward the center of that circle. The net force you are experiencing must also point toward the center of the circle, since net force causes acceleration. You experience a feeling of accleration in the direction opposite your acceleration.

Problem 27:

You're pushing your little cousin in a rocking chair. To make the chair rock farther and farther, you should only push it forward when it's

(A) on your side of its equilibrium position. [34.5% picked]

(B) on the far side of its equilibrium position. [8.4% picked]

(C) rocking away from you. [34.1% picked]

(D) rocking toward you. [21.2% picked]

Answer: (C) rocking away from you. [34.1% picked]

Why: To make the chair rock more strongly, you must transfer additional energy to it. You do that by doing work on the chair, which requires that it move in the direction that you push it. By pushing the chair away from you as it moves away from you, you do work on it and make it rock harder and harder.

Problem 28:

You toss your backpack directly upward and watch it rise to its peak height. At the moment that it reaches that peak height, its velocity is

(A) downward and its acceleration is zero. [4.0% picked]

(B) downward and its acceleration is downward. [4.4% picked]

(C) zero and its acceleration is downward. [86.7% picked]

(D) zero and its acceleration is zero. [4.9% picked]

Answer: (C) zero and its acceleration is downward. [86.7% picked]

Why: At the peak of its motion, the backpack is momentarily motionless so its velocity is zero. However, it continues to accelerate downward, like any object that is in free fall.

Problem 29:

You're playing soccer and the other team's goalie has kicked the ball directly toward you. You kick the ball back and score a goal. If the goalie had rolled the ball slowly toward you instead, how would that have affected the ball's speed after you kicked it with the same motion of your foot?

(A) The slower-moving ball would have traveled away from you faster after you kicked it because of its centripetal force. [2.7% picked]

(B) The slower-moving ball would have traveled away from you faster after you kicked it because its momentum wouldn't have to change as much to go back fast. [6.2% picked]

(C) The slower-moving ball would also have traveled away from you slower after you kicked it. [81.4% picked]

(D) The slower-moving ball would have traveled away from you faster after you kicked it because of the force of its momentum. [9.3% picked]

Answer: (C) The slower-moving ball would also have traveled away from you slower after you kicked it. [81.4% picked]

Why: The faster your leg is moving when the ball bounces off your leg, the greater the approach speed of the two objects before the bounce and the greater their separation speed after the bounce.

Problem 30:

You're a counselor at summer camp and your group of kids has talked you into jumping off the roof of the boathouse into the lake beneath it. You're secretly worried about hurting yourself when you hit the water, so you decide to make sure that your speed is a small as possible when you reach the water's surface. Of the following ways to leave the roof, which one will give you the smallest speed when you reach the water?

(A) Jumping upward as you walk off the roof. [6.6% picked]

(B) Running as quickly as possible off the roof. [4.4% picked]

(C) Hooking your toes around the edge of the roof and pulling yourself downward as you step off the roof. [40.7% picked]

(D) Walking as slowly as possible off the roof. [46.9% picked]

Answer: (D) Walking as slowly as possible off the roof. [46.9% picked]

Why: To impact the water at the slowest possible speed, you want to reach the water with the least possible kinetic energy. During your descent your gravitational potential energy will become kinetic energy, but you will also retain any kinetic energy that you started with. To minimize that initial kinetic energy, you should leave the roof traveling as slowly as possible. If you start at high speed, whether you are heading upward, forward, or downward (by pulling yourself downward with your toes), you will start with excess kinetic energy and therefore hit the water with more than the minimum kinetic energy and speed.