A snowball with a mass of 85 g hits the top hat of a 1.5 m tall snowman and sticks to it. the hat and the snowball, with a combined mass of 220 g, fall off together at a horizontal velocity 8.0 m/s.

a. how fast was the snowball moving before the impact?

b. how far from the snowman did the top hat land?

Part (a) : Velocity of the snowball

By conservation of momentu;

m1v1 + m2v2 = m3v3,

Where, m1 = mass of snowball, v1, velocity of snowball, m2 = mass of the hat, v2 = velocity of the hat, m3 = mass of snowball and the hat, v3 = velocity of snowball and the hut.

v2 = 0, and therefore,

85*v1 + 0 = 220*8 = > v1 = 220*8/85 = 20.71 m/s

Part (b) : Horizontal range

x = v3*t

But,

y = vy - 1/2gt^2, but y = - 1.5 m (moving down), vy = 0 (no vertical velocity), g = 9.81 m/s^2

Substituting;

-1.5 = 0 - 1/2*9.81*t^2

1.5 = 4.905*t^2

t = Sqrt (1.5/4.905) = 0.553 seconds

Then,

x = 8*0.553 = 4.424 m