A hovering mosquito is hit by a raindrop that is 40 times as massive and falling

Question

A hovering mosquito is hit by a raindrop that is 40 times as massive and falling at 8.3 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic?

Because a raindrop is "soft" and deformable, the collision duration is a relatively long

8.0 ms. What is the mosquito's average acceleration, in g's, during the collision? The peak acceleration is roughly twice the value you found, but the mosquito's rigid exoskeleton allows it to survive accelerations of this magnitude. In contrast, humans cannot survive an acceleration of more than about 10 g.

Explanation / Answer

Here ,

let the mass of mosquito is m

mass of water drop = 40 * m

let the final velocity after the collision is v

Using coservation of momentum

40 * m * 8.3 = (m + 40m) * v

v = 8.097 m/s

the speed of raindrop after the collision is 8.097 m/s

---------------

Now, time , t = 0.008 s

acceleration of the mosquito = v/t

acceleration of the mosquito = 8.097/0.008

acceleration of the mosquito = 1012.1 m/s^2 = 103.1 g's

the acceleration of the mosquito is 103.1 g's

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