A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
Given: Mass of the ball is 0 .15 kg , its initial speed is 54 kmh -1 and the ball is deflected at an angle of 45 ° .
The situation is shown in the figure below.
Here, AO is the original path of the ball, OB is the path followed by the ball after deflection. Angle AOB is the angle between the incident and deflected paths of the ball.
From the figure,
∠ A O P = ∠ B O P ∠ A O P + ∠ B O P = 45 ° ∠ A O P = 22.5 °
The horizontal components of velocities suffer no change. The vertical components of velocities are in the opposite directions.
Impulse imparted to the ball is given as,
I = m v cos θ − ( − m v cos θ ) = 2 m v cos θ
Where, m is the mass of the ball and v is the velocity of the ball.
By substituting the given values in the above expression, we get
I = 2 × 0.15 × 54 × 1000 3600 × cos 22.5 = 4.16 kgms − 1
Thus, the impulse imparted to the ball is 4.16 kgms − 1 .
Given: Mass of the ball is
The situation is shown in the figure below.
Here, AO is the original path of the ball, OB is the path followed by the ball after deflection. Angle AOB is the angle between the incident and deflected paths of the ball.
From the figure,
The horizontal components of velocities suffer no change. The vertical components of velocities are in the opposite directions.
Impulse imparted to the ball is given as,
Where,
By substituting the given values in the above expression, we get
Thus, the impulse imparted to the ball is
