2.) You and your friends are playing soccer. Your friend kicks a soccer ball at

Question

2.) You and your friends are playing soccer. Your friend kicks a soccer ball at 8m/s toward you. Instead of kicking it like normal, you decide to kick a slightly larger ball at it to make it reverse directions. They hit head on with a coefficient of restitution of 0.9

Can you solve showing all steps and equations?

a.) If the soccer ball has an inertia of 600g, how fast would the larger, 750g, ball have to be traveling to exactly reverse the soccer ball's velocity?

b.) what is the initial relative velocity of the two objects?

c.) What percentage of the original kinetic energy is convertible to some other form?

d.) what are the final velocities of both of the balls immediately after the collision?

Explanation / Answer

a) suppose intial velocity of larger ball is v.

then using momentum conservation for collision.

initial momentum of two ball system = final momentum

600 x 8 - 750 x v = (600 x -8) + (750 x vf)

vf = 12.8 - v

coefficient of restitition = velcoity of seperation / velocity of approach

0.9 = ( 12.8 - v + 8 ) / (v + 8 )

0.9v + 7.2 = 20.8 - v

v = 7.16 m/s

b) of soccer ball wrt to larger ball = velocity of soccer ball - velocity of larger ball

         = 8 - ( - v) = 8 + 7.16 = 15.16 m/s towards larger ball

of larger ball = 15.16 towards soccer ball

after collision.

soccer ball = -8 - (12.8 - v) = -20.8 - 7.16 = - 13.64 m/s

so 13.64 away

c) initial KE, KEi = (0.600 x 8^2 / 2 ) + (0.750 x 7.16^2 / 2)

        = 38.42 J

final KE, KEf = (0.600 x 8^2 / 2) + (0.750 x (12.8 - 7.16)^2 / 2)

   = 31.13 J

energy converted = 38.42 - 31.13 = 7.29 J

d) V_soccer = 8 m/s opposite of its initial direction

V_larger = 12.8 - 7.16 = 5.64 m/s in the direction of initial soccer velocity.

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