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Chapter 6: Problem 28

A hovering fly is approached by an enraged elephant charging at \(2.1 \mathrm{~m} / \mathrm{s}\). Assuming that the collision is elastic, at what speed does the fly rebound? Note that the projectile (the elephant) is much more massive than the target (the fly).

Short Answer

Expert verified
The fly rebounds with a speed of approximately 4.2 m/s.

Step by step solution

01

Understand Elastic Collision

In an elastic collision, momentum (mass x velocity) and kinetic energy are conserved. Considering the great mass difference between the elephant and the fly, the momentum change of the elephant is negligible.
02

Conservation of Momentum

In the case where the mass of one object is much greater than the other, during elastic collision, the smaller object rebounds with nearly twice the velocity of the larger object. Here, because the mass of the elephant is much higher than the fly, we can use this fact to find the speed of the rebounding fly.
03

Calculate the Speed of the Rebounding Fly

So, the speed of the rebounding fly will be nearly twice the velocity of the elephant, which is \(2 \times 2.1 \, m/s = 4.2 \, m/s\). This is assuming the collision is perfectly elastic and that the elephant does not slow down upon impact.

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