Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. One is a robust 250 g beast initially moving south at 20.0 cm/s, while the other is a svelte 150 g creature initially moving north at 60.0 cm/s. Calculate the decrease in kinetic energy that results from the collision.

Answer 1

Find the final combined velocity after the collision using conservation of momentum,
m1v1+m2v2 = (m1+m2)v
solve for v.

Compare kinetic energy before and after impact,
Before: (1/2)m1v1²+(1/2)m2v2²
after: (1/2)(m1+m2)v²

Answer 2

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