A batsman deflects a ball by an angle of 60⁰ without changing its initial speed of 20 ms^–1. What is the impulse imparted to the ball if its mass is 0.15 kg?

The batsman deflects a ball by an angle of 60° without changing its initial speed of 20m/s.

we have to find impulse imparted to the ball.

we know, impulse = change in linear momentum

here initial and final velocity vector v₁ and v₂ has same magnitude and angle between them is 60⁰ hence there difference is 2v sin$\left(\frac{\theta }{2}\right)$ where v is their magnitude.

hence impulse 2mvsin$\frac{\theta }{2}$

$2\times 0.15\times 20 \sin \left({30}^0\right)=3 \mathrm{kgm}/\mathrm{s}$