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Queens College, CUNY  ACTING 20
Chapter 6—Energy of a System
MULTIPLE CHOICE
1)A constant force of 12 N in the positive x direction acts on a 4
Queens College, CUNY  ACTING 20
Chapter 6—Energy of a System
MULTIPLE CHOICE
1)A constant force of 12 N in the positive x direction acts on a 4
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Queens College, CUNY  ACTING 20
Chapter 6—Energy of a System
MULTIPLE CHOICE
1)A constant force of 12 N in the positive x direction acts on a 4.0kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement?
a. +60 J
b. +84 J
c. +72 J
d. +48 J
e. +57 J
 A 5.0kg object is pulled along a horizontal surface at a constant speed by a 15N force acting 20? above the horizontal. How much work is done by this force as the object moves 6.0 m?
 78 J
 82 J
 85 J
 74 J
 43 J
 A 2.0kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?
a. +0.29 kJ
b. ?0.29 kJ
c. +30 J
 ?30 J
 ?50 J
 How much work is done by a person lifting a 2.0kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?
 0.22 kJ
 0.20 kJ
 0.24 kJ
 0.27 kJ
 0.31 kJ
 A 2.5kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm?
a. +2.0 J
b. +20 J
c. ?2.0 J
d. ?20 J
e. +40 J
 The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is W_{A}; that on B is W_{B}. Which statement is correct?
 W_{A} = W_{B}.
 W_{A} = W_{B}.
 W_{A} = 2 W_{B}.
 W_{A} = 4 W_{B}.
 W_{B} = 2 W_{A}.
 Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by
 W_{A} = 4 W_{B}.
 W_{A} = 2 W_{B}.
 W_{A} = W_{B}.
 W_{B} = 2 W_{A}.
 W_{B} = 4 W_{A}.
 When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction ?_{k}, then dragged back along the same path to its original position, the work done by friction is
 0.
 ??_{k}mgd.
c. +?_{k}mgd.
d. ?2?_{k}mgd.
e. +2?_{k}mgd.
 Planets go around the sun in elliptical orbits. The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the
right. F_{} and are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W_{} and . At the position shown

 W_{} slows the planet down; speeds it up.
 W_{} slows the planet down; does no work on it.
 W_{} speeds the planet up; does no work on it.
 W_{} speeds the planet up; slows it down.

 W_{} does no work on it; speeds the planet up.
 The work done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d is
 always negative.
 always positive.
 negative half the time, positive the other half of the time.
 positive more than it is negative.
 negative more than it is positive.
 A 30kg child sitting 5.0 m from the center of a merrygoround has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is
 0 J.
b. 150 J.
c. 1 500 J.
d. 4 700 J.
e. 46 000 J.
 Sally, who weighs 450 N, stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.
 The work Roger does on the skateboard is 0 J.
 The work Roger does on the skateboard is 1 300 J.
 The work Sally does on the skateboard is 1 300 J.
 The work Sally does on the skateboard is 5 850 J.
 The work Roger does on the skateboard is 5 850 J.
 Negative work can be done
 by friction on the tires while a car is accelerating without skidding.
 by a spring at the bottom of an elevator shaft when it stops a falling elevator.
 by a hand catching a ball.
 by all of the above.
 only by (b) and (c) above.
 Positive work can be done
 by friction on the tires when a car is accelerating without skidding.
 by a spring when it launches a clown in the air.
 by a hand throwing a ball.
 by all of the above.
 only by (b) and (c) above.
 A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P =
5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?
 2.7 J
 1.0 J
 2.2 J
 1.6 J
 3.2 J
 A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point m. How much work is done by the given force during this displacement?
a. +45 J
b. ?45 J
c. +30 J
 ?30 J
e. +75 J
 Two vectors and are given by and . If these two vectors are drawn starting at the same point, what is the angle between them?
a. 106?
b. 102?
c. 110?
d. 113?
e. 97?
 If , , and the angle between and (when the two are drawn starting from the same point) is 60?, what is the scalar product of these two vectors?
a. ?13
b. +13
c. +37
d. ?37
 73
 If vectors and have magnitudes 12 and 15, respectively, and the angle between the two when they are drawn starting from the same point is 110?, what is the scalar product of these two vectors?
a. ?76
b. ?62
c. ?90
d. ?47
e. ?170
 If the vectors and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is ?100, what is the magnitude of the sum of these two vectors?
a. 6.6
b. 4.6
c. 8.3
d. 9.8
e. 7.6
 If the scalar product of two vectors, and , is equal to ?3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130?, what is the magnitude
of

?

a.

2.1

b.

2.5

c.

2.3

d.

2.7

e.

3.1

 If , , and , what is the angle between the two vectors when they are drawn starting from the same point?
a. 118?
b. 107?
c. 112?
d. 103?
e. 77?
 Two vectors and are given by and . The scalar product of and a third vector is ?16. The scalar product of and is +18. The z component of is 0. What is the
magnitude of ? a. 7.8
b. 6.4
c. 3.6
d. 5.0
e. 4.8
 If = 10, = 15, and ? = 130?, determine the scalar product of the two vectors shown.
a. +96
b. ?96
c. +51
d. ?51
e. ?35
 If = 5.0, = 8.0, and ? = 30?, determine the scalar product of the two vectors shown.
a. ?35
b. +35
c. ?20
d. +20
e. +40
 If = 6.0, = 5.0, and ? = 40?, determine the scalar product of the two vectors shown.
a. +19
b. +23
c. ?19
d. ?23
e. +30
 If the scalar (dot) product of two vectors is negative, it means that
 there was a calculator error.
 the angle between the vectors is less than 90 degrees.
 the angle between the vectors is 90 degrees.
 the angle between the vectors is greater than 270 degrees.
 the angle between the vectors is between 90 and 180 degrees.
 After a skydiver reaches terminal velocity,
 the force of gravity no longer performs work on the skydiver.
 work performed by the force of gravity is converted into gravitational potential energy.
 gravitational potential energy is no longer available to the system of the skydiver plus the Earth.
 gravitational potential energy is converted into thermal energy.
 thermal energy is converted into gravitational potential energy.
 Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
a. and both lie along the positive x axis.
b. lies along the positive x axis. lies along the negative x axis.
c. and both lie along the positive y axis.
d. lies along the negative x axis. lies along the negative y axis.
e. lies along the positive y axis. lies along the negative y axis.
 An object moving along the x axis is acted upon by a force F_{x} that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?

 ?10 J
b. +10 J
c. +30 J
 ?30 J
e. +40 J
 A body moving along the x axis is acted upon by a force F_{x} that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m?

 ?2 J
 ?18 J
 ?10 J
 ?26 J
e. +18 J
 A force acting on an object moving along the x axis is given by F_{x} = (14x ? 3.0x^{2}) N where x is in m. How much work is done by this force as the object moves from x = ?1 m to x = +2 m?
a. +12 J
b. +28 J
c. +40 J
d. +42 J
 ?28 J
 The force an ideal spring exerts on an object is given by F_{x} = ?kx, where x measures the displacement of the object from its equilibrium (x = 0) position. If k = 60 N/m, how much work is done by this force as the object moves from x = ?0.20 m to x = 0?
a. ?1.2 J
b. +1.2 J
c. +2.4 J
d. ?2.4 J
e. +3.6 J
 A 1.5kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m?

 18 J
 21 J
 23 J
 26 J
 8 J
 Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at
the origin, and the dot product of the two vectors is . Which possibility is correct?
a. and both lie along the positive x axis.
b. lies along the positive x axis. lies along the negative x axis.
c. and both lie along the positive y axis.
d. lies along the negative x axis. lies along the negative y axis.
e. lies along the positive y axis. lies along the negative x axis.
 A 2.0kg particle has an initial velocity of m/s. Some time later, its velocity is m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?
 17 J
 49 J
 19 J
 53 J
 27 J
 A 4.0kg block is lowered down a 37? incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?

 ?58 J
 ?53 J
 ?68 J
 ?63 J
 ?47 J
 If the resultant force acting on a 2.0kg object is equal to N, what is the change in kinetic energy as the object moves from m to m?
a. +36 J
b. +28 J
c. +32 J
d. +24 J
e. +60 J
 As a 2.0kg object moves from m to m, the constant resultant force acting on it is
equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?

 62 J
 53 J
 73 J
 86 J
 24 J
 A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?
a. ?3.3 J
b. +1.3 J
c. +3.3 J
d. ?1.3 J
e. +4.6 J
 A 2.0kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

 27 J
 20 J
 24 J
 17 J
 37 J
 A 3.0kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37? above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?
a. ?34 J


b. ?64 J



c. ?30 J



d. ?94 J
e. +64 J





 A 10kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?
a. 0.85 m/s
b. 0.89 m/s
c. 0.77 m/s
d. 0.64 m/s
e. 0.52 m/s
 A 10kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P) acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

 8.3 J
 6.4 J
 7.0 J
 7.7 J
 3.9 J
 A 20kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 13 J. How much work is done by the frictional force on the block as it moves the 2.0 cm?
a. ?2.5 J
b. ?1.4 J
c. ?3.0 J
d. ?1.9 J
e. ?14 J
 The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m
a. 3.7 m/s


b. 4.4 m/s



c. 4.9 m/s



d. 5.4 m/s



e. 14 m/s


 A 2.0kg block situated on a frictionless incline is connected to a light spring (k = 100 N/m), as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

 76 cm/s
 68 cm/s
 60 cm/s
 82 cm/s
 57 cm/s
 A 2.0kg block sliding on a frictionless horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates?
 4.6 m/s
 5.3 m/s
 5.7 m/s
 4.9 m/s
 3.5 m/s
 A 10kg block on a rough horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position?
 4.5 J
 2.1 J
 6.9 J
 6.6 J
 4.9 J
 A 2.0kg body moving along the x axis has a velocity v_{x} = 5.0 m/s at x = 0. The only force acting on the object is given by F_{x} = (?4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?
 4.2 m
 3.5 m
 5.3 m
 6.4 m
 5.0 m
 The only force acting on a 1.6kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?

 52 J
 44 J
 36 J
 60 J
 25 J
 The only force acting on a 2.0kg body moving along the x axis is given by F_{x} = (2.0x) N, where x is in
m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m?
 4.2 m/s
 3.6 m/s
 5.0 m/s
 5.8 m/s
 2.8 m/s
 The only force acting on a 2.0kg body as it moves along the x axis is given by F_{x} = (12 ? 2.0x) N,
where x is in m. The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?

 36 J
 39 J
 43 J
 46 J
 30 J
 The only force acting on a 1.8kg body as it moves along the x axis is given by F_{x} = ?(3.0x) N, where x is in m. If the velocity of the body at x = 0 is v_{x} = +8.0 m/s, at what value of x will the body have a velocity of +4.0 m/s?
 5.7 m
 5.4 m
 4.8 m
 4.1 m
 6.6 m
 Carts A and B have equal masses and travel equal distances D on sidebyside straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest.
The velocities _{A} and _{B} of the bodies at the end of distance D are related by

 B = A .
 B = A.
 B = 2 _{A}.
 B = 4 _{A}.
 A = 2 _{B}.
 Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses M and 2M respectively. The relation between their speeds immediately after the work has been done on them is
 v_{A} = v_{B}.
 v_{A} = 2v_{B}.
 v_{A} = v_{B}.
 v_{B} = v_{A}.
 v_{B} = 2v_{A}.
 Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero.
 More work was done on A than on B.
 More work was done on B than on A.

 The amount of work is the same for both.
 It is meaningless to compare the amount of work because the forces were so different.
 Work was done on B, but no work was done on A because the wall did not move.
 The force of static friction exerted on an automobile's tires by the ground
 provides the accelerating force that makes the car move forward.
 does positive work on the car while it is accelerating.
 does negative work on the car while it is decelerating.
 does everything listed in (a), (b) and (c).
 only does positive or negative work as in (b) or (c).
 A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true?
 At maximum height the ball has its greatest kinetic energy.
 The horizontal component of the baseball’s kinetic energy is constant.
 The vertical component of the baseball’s kinetic energy is constant.
 The mechanical energy of the baseball is greater when nearer to the ground.
 No answer above is correct.
 When a ball rises vertically to a height h and returns to its original point of projection, the work done by the gravitational force is
 0.
 ?mgh.
c. +mgh.
d. ?2mgh.
e. +2mgh.
 Two balls, A and B, of mass m and 2m respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is
 one quarter the work done on A.
 one half the work done on A.
 the same as the work done on A.
 twice the work done on A.
 four times the work done on A.
 Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has
four times the mass of ball A. When the balls pass the bottom of a first floor window at height above the ground, the relation between their kinetic energies, K_{A} and K_{B}, is

 K_{A} = 4K_{B}.
 K_{A} = 2K_{B}.
 K_{A} = K_{B}.
 K_{B} = 2K_{A}.
 K_{B} = 4K_{A}.
 Two clowns are launched from the same springloaded circus cannon with the spring compressed the same distance each time. Clown A has a 40kg mass; clown B a 60kg mass. The relation between their kinetic energies at the instant of launch is
a.
.
b.
.
c. K_{A} = K_{B}. d.
.
e.
.
 Two clowns are launched from the same springloaded circus cannon with the spring compressed the same distance each time. Clown A has a 40kg mass; clown B a 60kg mass. The relation between their speeds at the instant of launch is
a.
.
b.
.
c. v_{A} = v_{B}. d.
.
e.
.
 In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?
 Block A has twice as much kinetic energy as block B.
 Block B has lost twice as much kinetic energy to friction as block A.
 Block B has lost twice as much kinetic energy as block A.
 Both blocks have had equal losses of energy to friction.
 No energy is lost to friction because the ground has no displacement.
 A mass attached to the end of a spring is pulled out and released on a surface with friction. The work
done on the mass by the force exerted by the spring

 never has the same sign as the change in energy owing to friction.
 always has the same sign as the change in energy owing to friction.
 has the same sign as the change in energy owing to friction during one half of each cycle.
 never has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.

 always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.
 The graph below shows how the force on a 0.500 kg particle varies with position. If the particle has
speed at x = 0.00 m, what is its speed in m/s when x = 8.00 m?
a. 2.00
b. 10.7
c. 14.8
d. 15.0
e. 21.1
 A 12kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?
a. 0.78 m/s
b. 0.81 m/s
c. 0.71 m/s
d. 0.58 m/s
e. 0.64 m/s
 A 7.0kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

 7.4 J
 5.4 J
 6.1 J
 6.7 J
 4.9 J
 Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs?

 2.9 cm
 5.0 cm
 5.8 cm
 7.5 cm
 10.0 cm
 A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy?
 It increases by 10 J.
 It decreases by 10 J.
 It increases, but not necessarily by 10 J.
 It decreases, but not necessarily by 10 J.
 It remains the same.
 A conservative force on a particle moving along the x axis is given by . Which of the following is a potential that is associated with this force?
a.
b.
c.
d.
e. No answer given above is correct.
 The force a spring exerts on a body is a conservative force because
 a spring always exerts a force opposite to the displacement of the body.
 a spring always exerts a force parallel to the displacement of the body.
 the work a spring does on a body is equal for compressions and extensions of equal magnitude.
 the work a spring does on a body is equal and opposite for compressions and extensions of equal magnitude.
 the net work a spring does on a body is zero when the body returns to its initial position.
 Which of the following is a conservative force? (All refer to a car on a slope.)
 The force you exert on the car pushing it uphill.
 The force exerted by rain drops falling on the car.
 The frictional force of the road on the car.
 The gravitational force acting on the car.
 The force you exert on the car (pushing it uphill) after it starts to slide downhill.
 For a force to be a conservative force, when applied to a single test body
 it must have the same value at all points in space.
 it must have the same direction at all points in space.
 it must be parallel to a displacement in any direction.
 equal work must be done in equal displacements.
 no net work must be done for motion in closed paths.
 A single conservative force F_{x} = (6.0x ? 12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m?
a. +11 J
b. +29 J
c. +9.0 J
d. ?9.0 J
e. +20 J
 As a particle moves along the x axis it is acted upon by a single conservative force given by F_{x} = (20 ? 4.0x) N where x is in m. The potential energy associated with this force has the value +30 J at the origin (x = 0). What is the value of the potential energy at x = 4.0 m?
 ?48 J
b. +78 J
c. ?18 J
d. +48 J
e. +80 J
 A 0.40kg particle moves under the influence of a single conservative force. At point A where the particle has a speed of 10 m/s, the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 J of work on the particle. What is the value of the potential energy at point B?
a. +65 J
b. +15 J
c. +35 J
d. +45 J
e. ?40 J
 As a 1.0kg object moves from point A to point B, it is acted upon by a single conservative force which does ?40 J of work during this motion. At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J. What is the potential energy at point B?
a. +72 J
b. +10 J
c. +90 J
d. +28 J
e. +68 J
 Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is
a.
mgl.
b. 3mgl. c.
mgl.
 6mgl.
 9mgl.
 A particle is subject to the potential . What is the value of the y component of the force on the particle at the point (x, y) = (2.0, 3.0)?
 24
b. ?24
c. 14
d. ?14
e. 28
PROBLEM
 A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30?. What is the kinetic energy of the baseball at the highest point of the trajectory?