Simple Nature - Light and Matter

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 impact?(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 at v x =73.3 mi/h.He throws horizontally. By what amount, d, does the ball drop bythe time it reaches home plate, L=60.0 ft away?√(a) First find a symbolic answer in terms of L, v x , and g.(b) Plug in and find a numerical answer. Express your answer inunits of ft. (Note: 1 ft=12 in, 1 mi=5280 ft, and 1 in=2.54 cm)√Problem 50.51 A batter hits a baseball at speed v, at an angle θ abovehorizontal.(a) Find an equation for the range (horizontal distance to wherethe ball falls), R, in terms of the relevant variables. Neglect airfriction and the height of the ball above the ground when it is hit.⊲ Answer, p. 930(b) Interpret your equation in the cases of θ=0 and θ = 90 ◦ .(c) Find the angle that gives the maximum range.⊲ Answer, p. 93052 In this problem you’ll extend the analysis in problem 51to include air friction by writing a computer program. For agame played at sea level, the force due to air friction is approximately(7×10 −4 N·s 2 /m 2 )v 2 , in the direction opposite to the motionof 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, findthe optimal angle and the resulting range. ⊲ Answer, p. 930(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. 930Problems 227