Question

A hovering mosquito is hit by a raindrop that is 50 times as massive and falling at 8.9 m/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

Answer:

v =  8.72 m/s

Explanation:

To find the speed of the raindrop joint to the mosquito, you take into account the momentum conservation law for an inelastic collision. Before the collision the total momentum of raindrop and mosquito must be equal to the total momentum of both raindrop and mosquito after the collision.

$m_1v_1+m_2v_2=(m_1+m_2)v$       (1)

v1: speed of the mosquito before the collision= 0 m/s (it is at rest)

v2: speed of the raindrop before the collision = 8.9 m/s

m1: mass of the mosquito

m2: mass of the raindrop = 50m1 (50 time more massive that the mosquito)

v: speed of both raindrop and mosquito after the collision

You solve the equation (1) for v and replace the values of the rest of the parameters:

$v=\frac{m_1v_1+m_2v_2}{m_1+m_2}=\frac{m_1v_1+50m_1v_2}{m_1+50m_1}\\\\v=\frac{0m/s+50(8.9m/s)}{51}=8.72\frac{m}{s}$

hence, after the inelastic collision the speed of the raindrop andmosquito is 8.72 m/s