Question

a vehicle of mass m moving without friction with speed v.suddenly, rain starts falling vertically(relative to the road) such that per unit time,mass b falls on the vehicle,comes to rest relative to it, and says within it. determine the vehicle velocity as a function of time, up to a time it can contain all the falling

Answer 1

Mass of vehicle is m

The velocity of the vehicle is v.

Mass falling per unit time = b

Mass that has fallen in time t = bt

Let velocity is u at this time.

By using linear momentum conservation,

$mv = (m+bt)u$

then, $u = \frac{m}{m+bt} v$