A projectile is launched from the origin with speed $ v $ at an angle $ \theta $ from the horizon. At the highest point in the trajectory, the projectile breaks into two pieces, $ A $ and $ B $ of masses $ m $ and $ 2 m $ respectively. Immediately after the breakup, piece $ A $ is at rest relative to the ground. Neglect air resistance. Which of the following sentences most accurately describes what happens next?

Question

A projectile is launched from the origin with speed $ v $ at an angle $ \theta $ from the horizon. At the highest point in the trajectory, the projectile breaks into two pieces, $ A $ and $ B $ of masses $ m $ and $ 2 m $ respectively. Immediately after the breakup, piece $ A $ is at rest relative to the ground. Neglect air resistance. Which of the following sentences most accurately describes what happens next?, Piece $ B $ will hit the gorund first, since it is more massive., Both pieces have zero vertical velocity immedialtely after th breakup, and therefore they hit the ground at the same time., Piece $ A $ will hit the ground first, because it will have a downward velocity immediatly after the breakup., There is no way of knowing which piece will hit the ground first, because not enough information is given about the breakup.

MARKS App · Accepted Answer

At the highest point before explosion the vertical component of velocity is zero. So, as per law of conservation of momentum, after explosion also the pieces will have the same vertical component of velocity. So, in the vertical direction they will be under free fall with zero initial velocity. Hence, they will hit the ground at the same time.

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