Question

A hovering mosquito is hit by a raindrop that is 40 times as massive and falling at 8.8 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

To solve this problem we will apply the concepts related to the conservation of momentum. We know that the initial momentum must be equivalent to the final momentum, and according to the information given, masses 1 and 2 are related by the size of one of the objects. So we have to,

$m_1u_1+m_2u_2 = (m_1+m_2)v_f$

$m_{1,2}$ = Mass of each object

$u_{1,2}$  = Initial velocity

But we have that

$m_1 = 40m_2$

And there is not initial velocity for the mosquito, then,

$40m *u_2 = (m+40m)*v_f$

$40m(8.8) = 41mv_f$

$v_f = \frac{40(8.8)}{41}$

$v_f = 8.58m/s$

Therefore the raindrop and the mosquito will fall to 8.58m/s