What is the Initial Velocity of the Racket in a Momentum Word Problem?

[Miike012]

momentum word problem...

Problem:
A tennis ball initially moves with a velocity of 30.0 m/s
horizontally to the right. A tennis racket strikes the ball,
giving it a velocity of 30.0 m/s to the left. Treat the
collision as elastic and the ball and racket as particles of
mass 0.0500= m1 kg and 0.500= m2 kg respectively.

Find the initial velocity of the racket:

My solution:

I'm going to use the equation:
Final (V) Ball = (m1 - m2) / (m1 + m2) * Ball(Vi)

The racket is going some initial speed Vi... but because this equation requires that the second object , the racket, be stationary I will assign a new speed for the ball... 30 + Vi,
then solve for Vi

-30 = (0.0500 - 0.500)/( 0.0500 + 0.500) * (30 + Vi)

-30/((0.0500 - 0.500)/( 0.0500 + 0.500)) - 30 = Vi = -6.66 m/s

However the answer in the book is... -3.00..

Some help please... thank you.

 

[Miike012]

am I going at it incorrectly?

 

[NascentOxygen]

In the collision, the ball undergoes a change of momentum, and the racket undergoes the same (but opposite) change in its momentum. The ball's speed after collision is the same as its speed before the collision, therefore we declare no energy loss in the ball.

Since it is stated that the collision is perfectly elastic (no energy loss), then the racket, too, is constrained to having the same speed after the collision as before the collision (but, of course, with a reversal in its direction of travel).

 

[Miike012]

Ok... well when I calculate final V for racket so I could compare to initial V.. I get 5.45454545454546... which is still wrong...

 

[NascentOxygen]

Ok... well when I calculate final V for racket so I could compare to initial V.. I get 5.45454545454546... which is still wrong...

Start anew. Follow the steps I outlined.

 

[Miike012]

Thank you.. I got it.. :)