Question

A typical raindrop is much more massive than a mosquito and falls much faster than a mosquito flies. How does a mosquito survive the impact? Recent research has found that the collision of a failing raindrop with a mosquito is a perfectly inelastic collision. That is, the mosquito is "swept up" by the raindrop and ends up traveling along with the raindrop. Once the relative speed between the mosquito and the raindrop is zero, the mosquito is able to detach itself from the drop and fly away. a) A hovering mosquito is hit by a raindrop that is 40 times as massive and failing at 8.2 m/s, a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic? b) 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 (g=9.8 m/s^2), 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 10g (10g=98m/s^2)

Answer 1

(a)

given that

U = 8.2 m/s

we know

M*U = (M + m)V

where M = 40 *m

so

V = M*U / (M+m)

V = 40*m*8.2 /41m

V = 8m/s

(b)

given that

dT = 8ms= 8*10^(-3) s

we know that

F = m*dV/dT

F = m*8/8*10^(-3)

F = 1000m

and

from above relationship

a = 1000 m/s^2

a = 1000/g = 1000/ 9.8 = 102.04 g's