what is the velocity of the ball just before it hit the board?

Question

the ball (160 grams) was approaching the bat with a horizontal velocity of 25m/s just before it hit the bat. the ball was struck hard which changed the horizontal velocity to 40m/s in the opposite direction. the bat was in contact with the ball for 10ms. the ball then hit the board on the ground with a strong thud and came to an abrupt halt. as the ball hit the board, 25% of the kinetic energy of the ball just before it hit the board got converted to sound energy, another 25% converted to heat and the remaining 50% got used in creating a dent on the board. what is the velocity of the ball just before it hit the the board? the sound energy emitted was 8 joules.

Answer 1

Here are the facts that are relevant:

• 25% of the kinetic energy of the ball just before it hit the board got converted to sound energy
• sound energy emitted was 8 joules

 

Let KE be the total kinetic energy of the ball as it hit the board:

 

     0.25*KE = 8 joules

     KE = 8/0.25

     KE = 32 joules

 

What is the velocity of the ball just before it hit the board?

 

     KE = (1/2)mv²

     32 joules = (1/2)mv²

 

m is the ball's mass (160 g = 0.160 kg) and v is the ball's velocity.  Solve for v.