please show steps and equations used 24. (II) A brother and sister live near a l

Question

please show steps and equations used

24. (II) A brother and sister live near a lake. In the middle of winter, when the lake is solidly and smoothly frozen, they play catch by sliding a rock back and forth between them across the ice. Ignore all friction. The mass of the two children is 40 kg each, and the rock has a mass of 2.0 kg. Each time the rock is given a push by the child who has just caught it, it leaves the hand with a speed of 1.0 m/s (relative to the hand). (a) The children are initially at rest, and the sister first slides the rock toward her brother. What is the initial motion of the sister after she releases the rock? (b) The brother receives the rock. What is his initial velocity after he has received it? (c) The brother then slides the rock to his sister. What is his velocity now? (d) The sister catches the rock. What is her velocity now? (e) Will either child ever have a speed such that the rock will never reach the other player? In other words, can the game go on forever?

Explanation / Answer

24. II)

mass of two children, m = 40 kg each

speed of rock relative to hand = u = 1m/s

mass of rock = 2 kg

a. initially

speed of sister away from the brother after pushing the rock = v

from momentum balance

40v = 2

v = 0.05 m/s

b. after recieving the rock, speed og brother v'

from conservation of momentum

2 = 40v'

v' = 0.05 m/s

c. after sliding the rock to sister brother's speed = v"

from momentum balance

41*v' = 40v" - 2

41*0.05 + 2 = 40V"

v" = 0.10125 m/s

d. after sister catches the rock her speed = v'"

hence

40*0.05 + 2 = 41*v'"

v'" = 0.09756 m/s

e. at any point of time the person throwing the rock will not have speed greater than the speed of the rocck and hence the game can gop on for ever

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