a tennis player hits a ball of mass 200 g,which is moving towards him with a velocity of 30m/s west. calculate the impulse of the ball.
b.the force the racket will exact on the ball if the time of contact is 0.2 seconds
To calculate the impulse of the ball, we can use the formula:
Impulse = Force × Time
a) First, let's find the impulse of the ball.
Impulse is equal to the change in momentum of the ball, which is given by:
Impulse = m × Δv
Where m is the mass of the ball and Δv is the change in velocity.
Since the tennis player hits the ball, the initial velocity (u) changes to a final velocity (v). Given that the mass of the ball (m) is 200 g (or 0.2 kg) and the initial velocity (u) is 30 m/s towards the west, we need to calculate the change in velocity (Δv).
Δv = v - u
Given that the final velocity (v) is 0 m/s (since the ball stops), we can calculate the change in velocity:
Δv = 0 - 30 = -30 m/s
Now, we can calculate the impulse:
Impulse = m × Δv
Impulse = 0.2 kg × (-30 m/s)
Impulse = -6 kg·m/s
Therefore, the impulse of the ball is -6 kg·m/s (remember, negative sign indicates the change in direction).
b) To calculate the force exerted by the racket on the ball, we use the equation:
Impulse = Force × Time
Given that the time of contact (t) is 0.2 seconds, and we already know the impulse (-6 kg·m/s), we can rearrange the equation to solve for force:
Force = Impulse / Time
Substituting the values:
Force = -6 kg·m/s / 0.2 s
Force = -30 N
Therefore, the force exerted by the racket on the ball is -30 Newtons (again, negative sign indicates the direction of force).