Question

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 when the mass of the ball is 0.15 kg?

Answer 1

Given; v = 54 km/h
or v = 54 × \(\frac{5}{18}\) = 15 m/s

As is clear from the adjoining diagram, that there is no change in momentum in Y-direction,
Therefore, Δp_y = 0
∴ I_y = 0
Change in momentum in X-direction
Δp_x = p₂ – p₁ = -mv cos 22.5° – mv cos 22.5°
or Δpx = -2 mv cos 22.5°
∴ Impulse, I_x = Δp_x
(From – Impulse-momentum theorem).
or I_x = -2mv cos 22.5°
= -2 × 0.15 × 15 × 0.9239
= -4.15755
= – 4.2 N.s.

Total impulse,
I = I_x + I_y
= -4.2 + 0 = – 4.2 N.s.
or I = – 4.2 N.s.
Here, the negative sign indicates that this impulse is acting in -X direction.
∴ Magnitude of impulse I = 4.2 N.s.