A ball of mass M//2 filled with a gas ( whose mass is M//2) is kept on a frictionless table . A bullet of mass m = M//4 and velocity v_(0)hat(i)penetrates the ball , and rests inside at t=0. Assume that the amount of gas emitted during the collision can be neglected. The compressed gas is emitted at a contant velocity v_(0)//2 relative to the ball and at an even rate k ( k is a positive constant ) . (a)What is the velocity of the ball after the collision with the bullet ?(b) Find the velocity of the ball v(t) as a function of time. Assume that the emission of gas starts at t=0. What is the final velocity of the ball ?

A ball of mass M//2 filled with a gas ( whose mass is M//2) is kept on

1.	A ball of mass M//2 filled with a gas ( whose mass is M//2) is kept on a frictionless table . A bullet of mass m = M//4 and velocity v_(0)hat(i)penetrates the ball , and rests inside at t=0. Assume that the amount of gas emitted during the collision can be neglected. The compressed gas is emitted at a contant velocity v_(0)//2 relative to the ball and at an even rate k ( k is a positive constant ) . (a)What is the velocity of the ball after the collision with the bullet ?(b) Find the velocity of the ball v(t) as a function of time. Assume that the emission of gas starts at t=0. What is the final velocity of the ball ?
Answer» ANSWER :(a) `(v_(0))/( 5) hat( i ) `, ( B ) ` v_(0) [ ( 1)/( 5) + ( 1)/( 2) LN ((m+M)/(m + M - kt)) ] hat( i ) `, ( C ) 4.55 `v_(0)`

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