Young Jeffrey is bored, and decides to throw some things out of the window for f

Question

Young Jeffrey is bored, and decides to throw some things out of the window for fun. But since he is also very curious, he decides to do so in a controlled way. Jeffrey takes a rock, his tennis ball, and one of his father's golf balls and sets them on the sill of an open window. Then he uses a flat board to carefully push them all out of the window at the same time. The 2nd story window is 13.0 feet above the ground, and all three objects hit the ground just 0.500 feet away from the base of the house at the same time, 0.899 seconds after they're dropped. The rock hits with a thud and stays put, but the other two objects bounce. After another 0.674 seconds, the tennis ball reaches a maximum height of 7.31 feet, while the golf ball is 10.2 feet off the ground and still rising. Both have travelled an additional 0.375 feet horizontally. Calculate the magnitude of the average velocity of each object during these 1.57 seconds. Which object has the largest instantaneous velocity at the end of this time period?

Explanation / Answer

1. Rock
1st time of flight=2h/g=2*13/32.15=0.899sec
range=0.5 ft

so velocity horizontal=0.5/0.899=0.556ft/sec
velocity vertical=2gh=2*32.15*13=28.91 ft/sec
avg vert vel of rock = integral of(vt)/1.57=integral of(gt dt)/1.57=(32.15(0.8992)/(2))/(1.57)=8.27 ft/sec
avg horizontal=0.556*0.899/1.57=0.318ft/sec

2.Golf

during 2nd flight vel=2gh=2*32.15*7.31=21.68ft/sec

avg vel vert of golf ball=(32.15(0.8992)/(2)+(32.15(0.6742)/(2))/1.57=

avg hor vel=0.556 ft/sec

3.Tennis

during 2nd flight
h=ut-0.5gt2
10.2=u(0.674)-0.5*32.15*(0.6742)
u=25.97 ft/sec

avg horizontal vel=0.556

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