# Physics - Center of Mass

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A baseball player uses a bat with mass mbat to hit a ball with mass mball. Right before he hits the ball, the bat's initial velocity is 36 m/s, and the ball's initial velocity is -20 m/s (the positive direction is along the positive x-axis). The bat and ball undergo a one-dimensional elastic collision. Find the speed of the ball after the collision. Assume that mbat is much greater than mball, so the center of mass of the two objects is essentially at the bat.

• Physics - Center of Mass -

u=36 m/s, v(o)= -20 m/s.
Imagine that the bat is at rest, and the ball is approaching to it at the releative velocity
v(x)= v(o)+u =20+36 =56 m/s.
Then in the bat’s frame of reference the ball bounces at the velocity 56 m/s directed in opposite direction. The velocity of the ball in the rigid frame is the sum of the relative velocity of the bounce and velocity of the moving frame of reference.
The projections on the x-axis;
v(x) = 2u(x) –v(ox),
u(x) = u.
v(ox) = -v(o) ,

v(x) = 2u+v(o)