Question

1. A box of mass M and height H with an open top of area A slides across a frictionless, icy surface of a frozen lake with a velocity V. It then starts raining. Assuming that the rain falls vertically with a speed w, the average raindrop has a diameter d, and n raindrops fall into the box per second, find the speed of the box as a function of time. If the rain continues to fall and doesn’t hit the edge of the lake before it reaches its final speed, what is the final speed of the box?

Answer 1

Diameter, d peed, w Height, H elocity of the box, V Mass, M Area, A Lake Surface The Momentum of the box before rain was falling is, After the rain is falling down, the mass of the box is changing with time as rain drops are collected in the box. The velocity of rain has no effect on the velocity in horizontal direction as it is vertical Here, ρ is the density of water Use the momentum conservation equation MV The final velocity is reached when the box is completely full of water MV