A juggler is in a room with a ceiling 3m above her hands. a. what initial vertic

Question

A juggler is in a room with a ceiling 3m above her hands.

a. what initial vertical velocity keeps a ball in the air longest?

b. If she tosses a ball up every 0.7 s , with each ball spending .5s in her hands between the time it is caught and the time it is tossed, how many balls can she juggle? how many could she juggle in a similar room on the moon?

c. While she juggles, her hands are about 35cm apart. What is the ratio of the horizontal velocity of balls thrown on the moon (always assuming the same height) as compared to those thrown on earth?

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Explanation / Answer

a) height = 3m

let initial velocity be u

u^2 = 2gs = 2*9.81*3

so u = 7.67 m/s

so t = u/a = 0.78 secs

initial vertical velocity keeps a ball in the air longest = 7.67 m/s

b) Ball flight time = 0.78*2 = 1.56 secs

0.7*x = 1.56

so x= 1.56/0.7 = 2.22

so she can toss 3 balls at a time

on moon

let initial velocity be u

u^2 = 2gs = 2*1.6*3

so u = 3.1 m/s

so t = u/a = 1.93 secs

so flight time = 2*1.93 = 3.86 s

0.7*x = 3.86

so x = 5.5

so she can toss 6 balls at a time on moon

c) 0.35 = Vh*1.56 (on earth)

on moon 0.35 = Vm*3.86

so ratio of horizontal velocities on moon to earth = Vm/Vh = (0.35/3.86)/(0.35/1.56) = 0.4

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