Question

A hovering mosquito is hit by a raindrop that is 50 times as massive and falling at 8.4 m/sm/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic

Answer 1

8.23 m/s

Step-by-step explanation:

M₁ = M

M₂ = 50M

u₁ = 0

u₂ = 8.4m/s

v₁ = v₂ = v

Since this is a perfectly inelastic collision,

M₁U₁ + M₂U₂ = M₁V₁ + M₂V₂

the drop of rain and the mosquitoe sticks together after collision and have a common velocity after collision.

therfore,

v₁ = v₂ = v

0 + M₂U₂ = M₁V₁ + M₂V₂

but v₁ = v₂ = v

M₂U₂ = (M₁ + M₂)V

V = (M₂U₂) / (M₁ + M₂)

V = (50 * 8.4) / (50 + 1)

V = 420 / 51

v = 8.23m/s

The common velocity after impact is 8.23m/s