Answer:
(a) The speed of the racket immediately after the impact is -8.7 m/s
(b) The average force that the racket exerts on the ball is 0.471 N
Explanation:
Given;
mass of racket, m₁ = 1000 g = 1 kg
initial speed of racket, u₁ = -12 m/s (negative because it swings backwards)
mass of tennis, m₂ = 60g = 0.06 kg
initial speed of tennis, u₂ = 15 m/s
final speed of the tennis ball, v₂ = -40 m/s (negative because it moved backwards)
(a) How fast is her racket moving immediately after the impact?
Let the final speed of the racket = v₁
Apply the principle of conservation of linear momentum
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
1 x (-12) + (0.06 x 15) = (1 x v₁) + 0.06 x (-40)
-12 + 0.9 = v₁ - 2.4
-11.1 = v₁ - 2.4
v₁ = -11.1 + 2.4
v₁ = -8.7 m/s
The speed of the racket immediately after the impact is -8.7 m/s
The final speed of the racket is still backwards but at a lower speed.
(b) The average force that the racket exerts on the ball during 7 s in contact with the ball;
The average force the racket exerts on the ball is on the right