Impulse Imparted to the Ball

The impulse imparted to the ball can be calculated using the principle of conservation of linear momentum. When a batsman deflects a ball, the change in momentum of the ball is equal to the impulse imparted.

Given Data:
- Angle of deflection: 90 degrees
- Speed of the ball: 54 km/hr

Calculations:
1. Convert the speed of the ball from km/hr to m/s:
54 km/hr = 54 * 1000 m / 3600 s = 15 m/s

2. Since the angle of deflection is 90 degrees, the change in momentum is equal to the initial momentum of the ball:
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity

3. The impulse imparted to the ball can be calculated as the difference between the final momentum and initial momentum:
Impulse = Final momentum - Initial momentum

4. Since the speed of the ball remains the same after deflection, the final velocity of the ball is also 15 m/s.

5. Substitute the values into the impulse formula to find the impulse imparted to the ball.

Result:
The impulse imparted to the ball when the batsman deflects it by an angle of 90 degrees without changing its speed (54 km/hr) is calculated using the above steps. The final calculated value represents the impulse imparted to the ball.