Question

20 raindrops fall on an umbrella. The following day, 10 hail stones fall on the umbrella. All drops of rain and hail are of equal mass m and are traveling at the same velocity v. Both of these (rain and hail) fall on the umbrella in 1 second. What can we say about the Force exerted on the umbrella to hold it up

Answer 1

the force exerted by the umbrella against the drops is the same in both cases

Step-by-step explanation:

In this exercise the total mass of the raindrops and the hail are equal, therefore the momentum that these drops create is

raindrops I₁ = ∫ F dt

hail I₂ = ∫ F dt

since the mass and the velocity is the same the force is the weight of the drops

F = mg

whereby the impulse is

I₁ = mg t

I₂ = mg t

we can see that the impulses generated by hail and raindrops are equal, therefore the force exerted by the umbrella against the drops is the same in both cases