A tennis player hits a ball of mass 100g hard with the racket as a result of which the velocity of the ball changed from 2 m/s due east to 4 m/s due west within 0.01 s. What is the force of impact?
Question
A tennis player hits a ball of mass 100g hard with the racket as a result of which the velocity of the ball changed from 2 m/s due east to 4 m/s due west within 0.01 s. What is the force of impact?
Solution
Sure, let's solve this step by step:
Step 1: Identify the given values
- Initial velocity (u) = 2 m/s (due east)
- Final velocity (v) = 4 m/s (due west)
- Time (t) = 0.01 s
- Mass (m) = 100 g = 0.1 kg (since 1 kg = 1000 g)
Step 2: Calculate the change in velocity Since the direction of the velocity changes, we consider one of the velocities as negative. Let's consider the initial velocity as negative because it's in the opposite direction to the final velocity. So, change in velocity (∆v) = v - u = 4 m/s - (-2 m/s) = 6 m/s
Step 3: Calculate the acceleration Acceleration (a) = ∆v / t = 6 m/s / 0.01 s = 600 m/s²
Step 4: Calculate the force Force (F) = m * a = 0.1 kg * 600 m/s² = 60 N
So, the force of impact is 60 Newtons.
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