In a volcanic eruption, a 2400-kg boulder is thrown vertically upward into the air. At its highest point, it suddenly explodes into two fragments, one being three times the mass of the other. The lighter fragment starts out with only horizontal velocity and lands 274 m directly north of the point of the explosion. Where will the fragment land? Neglect any air resistance.

91.33 m towards the south

Explanation:

At the highest point , the boulder will be at rest so its velocity will be zero . When it explodes into two fragments , momentum in horizontal direction will be conserved since there is no external force in horizontal direction . So

m₁ v₁ = m₂ v₂

m₁ v₁ = 3m₁ v₂

v₁ = 3 v₂

So velocity of larger fragment will be  1 / 3  times the velocity of smaller  one , in horizontal direction , to conserve momentum.

The smaller fragment  travels a distance of 274 m horizontally in the north , the larger fragment will travel 274 / 3 or 91.33 m towards the south. It is so because time of fall for both is same , Or they travel in horizontal direction during the same time.

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