Answer:
The velocity of the tennis racket after the collision 14.966 m/s.
Step-by-step explanation:
let the following:
m₁ = mass of tennis racket = 0.311 kg
m₂ = mass of the ball = 0.057 kg
u₁ = velocity of tennis racket before collision = 30.3 m/s
u₂ = velocity of the ball before collision = -19.2 m/s
v₁ = velocity of tennis racket after collision
v₂ = velocity of the ball after collision
Right (+) , Left (-)
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.
So, the total kinetic energy before collision = the total kinetic energy after collision.
So, 0.5 m₁ u₁² + 0.5 m₂ u₂² = 0.5 m₁ v₁² + 0.5 m₂ v₂² ⇒ (1)
Also, the total momentum before collision = the total momentum after collision.
So, m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂ ⇒ (2)
Solving (1) and (2):
∴ v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)
= ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)
= 14.966 m/s.
So, the velocity of the tennis racket after the collision 14.966 m/s.
