Answers for Problem Set 3

Chapter 2

28.

(a) v = 0 at t = +- 2 [sqrt(3) ] / 3.
(b) a = 0 at t = 0
(c) a < 0 when t > 0; a > 0 when t < 0

57.
a_p = (v_L0 - v_p0)² / ( 2 x_L0)

    = 3.26 ft/sec²

p refers to the passenger train and L to the locomotive; x_L0 is the initial distance between the two. Deceleration has been taken positive.

58. The two trains would have travelled a total of 200 m + 800 m = 1000 m if they had not collided at 950 m.

72. Proof.

Chapter 4

(a) All have the same time of flight.
(b) All are the same.
(c) c-b-a are in order of decreasing horizontal component of velocity.
(d) c-b-a are in order of decreasing initial speed.

38. The death was not by falling accidentally, since the necessary horizontal component of velocity at the window would be implausibly high, 6.7 ft/sec. Of course, this speed is a bit high for being pushed, also. Maybe the body was brought to the site after a fall somewhere else.

53. Let d be the height at which the ball is hit, h be the height of the net, x be the player's distance from the net, and theta be the angle below the horizontal of the initial velocity ( v₀ ) of the ball. Then the ball clears the net by

z = - h + d - x tan (theta) - ( 1/2 ) g x² / [v₀ cos (theta) ]²
z = 0.2 m if the ball starts horizontally and 0.86 m below the top of the net if the ball starts out 5 degrees below the horizontal.

54 R = 715 m, or 25 m further than in the sample problem

56. The ball must be kicked between 31^o and 63^o above the horizontal. You get a quadratic equation for cos² (theta), which is best found and solved by a symbolic-algebra package.

IV.

(a) The distance   y = w [v_b sin(theta) + v_r)] / [v_b cos(theta)].    Theta is positive if he rows downstream.

(b) The time   T = w / [v_b cos(theta)].    Part (b) must be done before, not after, part (a)