Chapter 3 Solutions
Answers to Questions
Q1 Yes. Upon being dropped, the paper goes from zero velocity to some velocity downward.
Q2 No. The motion is one of constant velocity since the ball moves equal distances in equal times.
Q3 Yes. A has positive acceleration (speeding up).
B has negative acceleration (slowing down).
Q4 Both will fall with the same acceleration.
Q5 The crumpled one will be less affected by air resistance and will reach the floor first.
Q6 Because there is no air resistance in the evacuated tube, both the crumpled and the uncrumpled sheets of paper will reach the bottom of the tube at the same moment.
Q7 In the absence of air friction, Aristotle was wrong. In the presence of air friction, the shape and mass of the object can both affect the acceleration of a falling object. It is possible for a heavy object to fall slower than a light object and vice versa.
Q8 The distance traveled in a 0.10 s interval just before it hits the water will be greater than just after it is dropped because the velocity will have increased.
Q9 No. Constant acceleration would require the v vs. t curve to be a straight line. It shows curvature for the same time. (Acceleration is increasing.)
Q10 a. The thrown ball will reach the ground first. This is because its increase in velocity due to gravity though equal to that of the dropped ball is in addition to its initial velocity. The initial velocity continues to move the ball downward at a constant rate which adds to the amount of distance traversed because of the acceleration.
b. No. The only acceleration is that due to gravity which is the same for both balls.
Q11 The direction of the velocity vector during this time is upward. The direction of the acceleration vector is downward. Acceleration does not decrease. The decrease in the magnitude of the velocity is a direct result of the constant, Earthward directed acceleration.
Q12 Yes. The velocity of the rock was decreasing as it ascended. Thus more time was needed to traverse an equal distance when it was traveling more slowly.
Q13 The velocity changes direction at the apex (top) of the trajectory.
velocity
time
Q14 No, acceleration is due to gravity that has not gone away!
Q15 No. Acceleration is in the downward direction throughout the motion.
Q16 The acceleration will be constant (and never zero) because it is due to gravity. The velocity will not be constant decreasing on the way up, reaching zero then increasing as the ball rolls back down the incline.
Q17 Both reach the floor at the same time. They both have the same initial zero y-component of velocity, undergo the same acceleration, and drop the same vertical distance. The horizontal part of the motion is immaterial.
Q18 The rolled ball has the larger velocity. In addition to the vertical component (which is the same as that of the dropped ball), it has a horizontal component that the dropped ball lacks.
Q19 Of course. Horizontal velocity is not influenced by vertical velocity. For example, a kicked ball has both horizontal and vertical velocity. The only change in velocity comes from acceleration due to gravity.
Q20 Yes. Although the horizontal component remains constant, the vertical component increases downward. This changes the resultant vector that is determined by both magnitude as well as the vertical component of direction. (See figures below.)
Q21 No. Horizontal velocity has no influence on the vertical motion.
Q22 Above. The sights have been adjusted to compensate for the bullet's drop at great distance. It will be an over compensation for firing at a near target.
Q23 The higher trajectory takes longer. The time of flight is determined by the initial vertical velocity component which also determines the maximum height reached.
Q24 As there is always a horizontal velocity component not equal to zero, there is no time when the velocity of the ball is equal to zero for either of the shown trajectories.
Q25 The ball with the higher velocity is more likely to have been thrown by the fielder with the stronger arm.
Q26 No. The higher angled shot spends its time slowing its higher ascent until it stops and descends toward the ground
Q27 No. Even though its horizontal velocity component is greater than that of the other shot, it falls sooner to the ground.
Q28 A. The shot in direction C will not clear the chair; in order for the shot in direction B to clear the chair it will have to have a fairly high initial velocity that would likely cause it to overshoot the basket.
Q29 Insufficient magnitude will result in the ball falling short of its goal (regardless of direction). Too great a magnitude will result in the well-aimed shot overshooting the basket.
Q30 The arched shot has the advantage of giving the shooter more leeway in getting the shot through the hoop—a wider range of trajectories that will make it.
Q31 The likelihood of undershooting the basket becomes more likely with distance from the basket.
Q32 A hard low trajectory throw will reach the receiver in a shorter time interval and thus more unlikely to be intercepted. However, this type of throw places a greater demand on the requirement that the receiver accurately judges the moment and place that they and ball will arrive at the catching point.
Answers to Exercises
E1 a. 8 m/s
b. 16 m/s
E2 a. 3.2 m
b. 12.8 m
E3 50 m/s = 112 MPH
E4 a. 0.75 s
b. 2.76 m
E5 22 m/s
E6 30 m/s
E7 a. +5 m/s up
b. - 5 m/s down
E8 a. 10 m
b. 10 m
E9 1.5 s
E10 a. 6 m/s
b. 6 s
E11 a. 0.1667 s
b. 13.9 cm
E12 2.4 m
E13 1.25 m
E14 a. - 6 m/s
b. 5 m/s
E15 a. 1.0 s
b. 6 m
E16 a. 3 s
b. 90 m
Answers to Synthesis Problems
SP1 a. 0
b. 1.6 s
c. 12.8 m
d. 12 m
e. The ball is moving down.
SP2 a. vA = 15 m/s vB = 27 m/s
b. yA = 11.25 m yB = 29.25 m
c. No. Each has the same acceleration, hence, the rate of change of their velocity is the same.
SP3 a. 0.4 s
b. XA = 1.2 m; XB = 2.0 m
c. No. Ball B will reach the edge of the tabletop first and will begin its downward fall before Ball A. Since they each have the same downward acceleration, Ball A cannot catch Ball B.
SP4 a. t30 = 40 s
b. x = 13,840 m
c. t60 = 69.2 s
x = 13,840 m; Same as for the first angle.
SP5 a. 40.2 m/s
b. 18.3 m
c. 0.455 s
d. 1.03 m
SP6 a. 0. 65 seconds ()
b. 2.113 m ()
c. -0.1625m = -16.25 cm (2.113m-1.95m= 0.1625m), she misses!
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