A particle of mass 2 kg is projected with speed 20 m/s at 30° above the horizontal and returns to the same level. Neglect air resistance. If the magnitude of the total impulse due to gravity during the complete flight is N N·s, find N.
Physics · Center of maas , Momentum and Collision · impuse and question based on it
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Question

A particle of mass 2 kg is projected with speed 20 m/s at 30° above the horizontal and returns to the same level. Neglect air resistance. If the magnitude of the total impulse due to gravity during the complete flight is N N·s, find N.

Physics · Center of maas , Momentum and Collision · impuse and question based on it

G1 Physics · Accepted Answer

Impulse due to gravity equals the change in momentum of the projectile over the complete flight. The horizontal velocity is unchanged. The initial vertical velocity is +20sin30° = +10 m/s and the final vertical velocity just before landing is −10 m/s. Hence change in vertical velocity is −20 m/s. Therefore Δp = mΔv = 2(−20) = −40 kg·m/s in the vertical direction. The magnitude of the impulse is 40 N·s, so N = 40.