Impulse And Momentum

Impulse equals the change in linear momentum of a body, expressed as $J=\Delta p=m(v_f-v_i)$, and it acts in the direction of that momentum change. Taking the initial direction of approach as positive, the incoming velocity is $+20\text{ m/s}$ and the rebound velocity is $-20\text{ m/s}$ because the ball reverses direction. The change in velocity is therefore $-20-20=-40\text{ m/s}$ in magnitude 40 m/s. Hence $J=0.15\times 40=6\text{ N s}$. The value 3 N s wrongly uses a velocity change of only 20 m/s, ignoring the reversal. The 4.5 N s value comes from an incorrect 30 m/s difference. The 0 N s choice mistakenly assumes equal speeds mean zero change, but direction reversal makes the momentum change largest. This follows the NCERT impulse-momentum theorem central to the Laws of Motion. As a sign check, the impulse points opposite to the incoming ball, exactly the direction in which the bat strikes.