A 50 kilogram boy with a bag full of rocks (the total mass is 50kg including the

Question

A 50 kilogram boy with a bag full of rocks (the total mass is 50kg including the boy and all the rocks) is standing in the middle of an ice covered frictionless pond. He takes out a 0.03 kg rock and throws it forwards with a speed of 15 m/sec at an angle of 30 degrees. Determine the velocity of the boy after he throws this rock. If the boy wanted to stay in place after throwing the rock, what would the necessary force of friction? If the time it took for the boy to reach your calculated velocity was 0.1 seconds, determine the impulse.  

Explanation / Answer

here,

mass of the boy is m = 50kg

mass of rock , mr = 0.03 kg

speed of rock , v1 = 15 m/s

theta = 30 degree

let the velocity of boy be v2

using conservation of momentum

m*v2 = mr*v1 * cos(30)

50 * v2 = 0.03 * 15 * 0.866

v2 = 7.79 * 10^-3 m/s

the velocity of the boy after he throws this rock is 7.79 * 10^-3 m/s

(b)

the frictional force required to the boy wanted to stay in place after throwing the rock be F

the time taken for the force is t

t = 0.1 s

force , F = change in momentum /time

F = 0.03 * 15/0.1

F = 4.5 N

the frictional force required to the boy wanted to stay in place after throwing the rock is 4.5 N

(c)

impulse = change in momentum

impulse = 0.03 * 15

impulse is 0.45 kg.m/s

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