river throw her out horizontally over the falls. Bill paddles a kayak,
adding an extra 10 km/hr to his velocity. They go over the edge
of the falls at the same moment, side by side. Ignore air friction.
Explain your reasoning.
(a) Who hits the bottom first?
(b) What is the horizontal component of Wendy’s velocity on im-
pact?
(c) What is the horizontal component of Bill’s velocity on impact?
(d) Who is going faster on impact?
50 A baseball pitcher throws a pitch clocked atvx= 73.3 miles/hour.
He throws horizontally. By what amount,d, does the ball drop by
the time it reaches home plate,L= 60.0 feet away?
(a) First find a symbolic answer in terms ofL,vx, andg.
√(b) Plug in and find a numerical answer. Express your answer
in units of ft. (Note: 1 foot=12 inches, 1 mile=5280 feet, and 1
inch=2.54 cm)
√Problem 50.51 A batter hits a baseball at speed v, at an angle θabove
horizontal.
(a) Find an equation for the range (horizontal distance to where
the ball falls),R, in terms of the relevant variables. Neglect air
friction and the height of the ball above the ground when it is hit.
.Answer, p. 1064
(b) Interpret your equation in the cases ofθ=0 andθ= 90◦.
(c) Find the angle that gives the maximum range.
.Answer, p. 1064
52 In this problem you’ll extend the analysis in problem 51
to include air friction by writing a computer program. For a
game played at sea level, the force due to air friction is approxi-
mately (7× 10 −^4 N·s^2 /m^2 )v^2 , in the direction opposite to the motion
of the ball.The mass of a baseball is 0.146 kg.
(a) For a ball hit at a speed of 45.0 m/s from a height of 1.0 m, find
the optimal angle and the resulting range. .Answer, p. 1064
(b) How much farther would the ball fly at the Colorado Rockies’
stadium, where the thinner air gives 18 percent less air friction?
.Answer, p. 1064
Problems 231