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

In summary, the problem involves a collision between a tennis ball and a racket, both with given masses and initial velocities. Assuming an elastic collision, the final velocity of the ball is the same as its initial velocity, and the final velocity of the racket is equal to its initial velocity but in the opposite direction. By using the equation for conservation of momentum, the initial velocity of the racket can be calculated to be -3.00 m/s.
  • #1
Miike012
1,009
0
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.
 
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  • #2


am I going at it incorrectly?
 
  • #3


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).
 
  • #4


Ok... well when I calculate final V for racket so I could compare to initial V.. I get 5.45454545454546... which is still wrong...
 
  • #5


Miike012 said:
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.
 
  • #6


Thank you.. I got it.. :)
 

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

What is momentum and how is it calculated?

Momentum is a physics concept that describes the quantity of motion an object has. It is calculated by multiplying an object's mass by its velocity.

Can momentum be negative?

Yes, momentum can be negative. This occurs when an object is moving in the opposite direction of its positive direction, as defined by the chosen reference frame.

How is momentum conserved in a closed system?

In a closed system, the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction. This is known as the law of conservation of momentum.

Why is momentum an important concept in physics?

Momentum is important because it helps us understand the behavior of moving objects and how they interact with each other. It is also a crucial concept in understanding the laws of motion and conservation of energy.

How is momentum different from velocity?

Velocity is a measure of an object's speed and direction, while momentum is a measure of the object's mass and velocity combined. Velocity can change if the speed or direction of an object changes, but momentum remains constant unless acted upon by an external force.

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