A tennis ball initially moves with a velocity of 27.0 m/s horizontally to the right. A tennis racket strikes the ball, giving it a velocity of 27.0 m/s to the left. Treat the collision as elastic and the ball and racket as particles of mass 0.0580 kg and 0.272 kg respectively.

Find the intial velocity of the racket.
Please help Im stuck

1 answer

This is an elastic impact problem.
Impact problems have one available equation, namely conservation of momentum.

m1u1+m2u2=m1v1+m2v2.
u, v represent initial and final velocities respectively, and m1, m2 are masses of bodies involved.
Note that velocities have signs, e.g. positive to the right, negative to the left, etc.

For elastic impacts, there is an additional equation, namely the conservation of energy.
Using the same notations above, we have
(1/2)m1u1²+(1/2)m2u2²=(1/2)m1v1²+(1/2)m2v2²

Since m1, m2, u1, v1 are given, these two equations will help you solve for u2 and v2.

For more explanations and examples, see:
http://www.efm.leeds.ac.uk/CIVE/CIVE1140/section04/elastic_impact.html
or
http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html