The masses of Chuck and Jackie are both m1. Chuck then picks up a motionless bal

Question

The masses of Chuck and Jackie are both m1. Chuck then picks up a motionless ball of mass m2, and throws it to Jackie so that after it leaves his hand, the speed of the ball relative to chuck is v0.

A) During this throw, what is the total impulse by all external forces applied to the system of Chuck and the ball?

B) After the throw, what is the speed of the ball with respect to the ground in terms of m1, m2, and v0, or a subset of these qualities?

C) After the throw, what is the speed of Chuck with respect to the ground?

D) Jackie then catches the ball. During that catch, what is the total impulse by all external forces applied to the system of Jackie and the ball?

E) After she catches the ball, what is Jackie's speed with respect to the ground?

F) In the end, what is Jackie's speed with respect to Chuck?

Explanation / Answer

A) The net force acting on the system containing both Chuck & ball = 0

so the total impulse by all the external forces on the system of Chuck & ball = 0

B) conserving momentum of the CHuck & ball system

Let velocity of Chuck after throwing be v_C

so given vel of ball relative to chuck = v0

so absolute velocity of ball = v0 + v_C

conserving momentum

m1 * v_C + m2*(v0 + v_C) = 0

so .. v_C*(m1 + m2 ) = - m2*v0

so.. v_C = - v0 * m2 / ( m1 + m2 )

so velocity of ball w.r.t ground = v0 + v_C = v0 * m1 / ( m1 + m2 )

C ) velocity of chuck w.r.t ground = v_C = - v0 * m2 / ( m1 + m2 )

so speed = v0 * m2 / ( m1 + m2 )

D)

Again as in (A)

The net force acting on the system containing both Jackie & ball = 0

so the total impulse by all the external forces on the system of Jackei & ball = 0

E)

Let jackie's speed w,r,t ground after catching be v_J

so conserving momentum

(m1 + m2 ) * v_J = m1*m2 *v0 / (m1 + m2 )

so .. v_J = v0 * m1*m2 / ( m1 + m2 )^2

F)

speed of Jackie w.r.t Chuck = v_J - v_C = v0 * m1*m2 / ( m1 + m2 )^2 + v0 * m2 / ( m1 + m2 )

= (v0 * m2 / ( m1 + m2 )^2 ) * [ m1 + m1 + m2 ]

= v0 * m2 * ( 2m1 + m2 ) / ( m1 + m2 )^2

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