For this question,assume that all velocities are horizontal and that there is no friction.Two skaters A and B are on an ice surface.A and B have the same mass M = 90.5 kg.A throws a ball with mass m = 200 g toward B with a speed v = 21.5 m/s relative to the ice.B catches the ball and throws it back to A with the same speed.After A catches the ball,his speed with respect to the ice is A)4.3 $\times$ 10³ m/s B)4.3 m/s C)4.8 $\times$ 10^-2 m/s D)9.5 $\times$ 10^-2 m/s E)0.34 m/s

Question

Quizplus · Accepted Answer

By conservation of momentum in the horizontal direction, the momentum of the system (A, B, and the ball) remains constant throughout the interaction. Therefore, we can write:
mAva + mBvb + mballvball = mAvf + mBv′ + mballv′ball
where Av is A's initial velocity, vb is B's initial velocity (0), vball is the ball's initial velocity, vf is A's final velocity, and v′ball is the ball's velocity after B throws it back. Since Av and vb are both zero, we can simplify to:
(mball/mA + mB)vball = (mball/mA + mB)v′ball
Plugging in the numbers, we have:
(0.2/90.5 + 90.5)(21.5) = (0.2/90.5 + 90.5)v′ball
Solving for v′ball, we get:
v′ball = 21.5/(0.2/90.5 + 90.5) = 4.3 m/s
Therefore, A's final velocity with respect to the ice is also 4.3 m/s.

For This Question,assume That All Velocities Are Horizontal and That ×\times×

For This Question,assume That All Velocities Are Horizontal and That $\times$