Why Do My Momentum Problem Solutions Differ from the Textbook Answers?

[neelakash]

I did the following two questions of the same category.But the answer is not matching.Please see if I went wrong.

Homework Statement

1.During rainfall,2000 hailstones per square metre (radius 0.5 cm) falls onto a 10mx10x roof with velocity 20m/s.FInd the average force exerted onto the roof without rebound.Density of hailstones 900kg/m3

2.A ball of mass m is dropped onto the ground from a certain height.Colliding elastcally,it again rises to that height.Again it falls.What is the force exerted onto the grond in a long interval of time?

Homework Equations

I think in both cases we may use this standard equation:
P=F_ext+u(dM/dt) where u is the relative velocity

The Attempt at a Solution

(1) In problem (1),the total mass is 30*pi.You may check it.
So,total force exerted on the roof
F=F_floor+F_gravity
Taking magnitudes---
=u(dM/dt)+Mg
=20*30*pi+30*pi*g (where g is the acceleration due to gravty).
~2808N
whereas the book says it is 1900 N
I noted that if we neglect the gravity term,the answer (1885N) is close to 1900N

(2)Here what I got is

F=F_floor+F_gravity
Taking magnitudes,-
=u(dm/dt)+mg
=d(mu/dt)+mg
since the u has not been giveen,I could not proceed more.
However,they have provided the answer mg.

 

[neelakash]

OK,first part is clear.They referred to terminal velocity.Hence,the term "average".So,F_ext=0