Question

A snow ball of mass 5 [kg] is hurled at a snow mobile of mass 1,000 [kg] that rest on a very smooth (frictionless) icy surface. The ice is level.
a. The snow ball sticks to the snow mobile, that then moves at a speed of 7 [cm] per second. Assuming no frictional forces between the snow mobile and the snow, what was the ball's initial velocity?
b. If a 5 kg “superball” with the same initial speed hit the stationary snowmobile instead of the snowball, would the snowmobile move faster or slower than in the case of the snowball? Use an equation or a drawing of vector to support your answer.

Answer 1

(a) Mass of the snow ball, m1 = 5 kg

Mass of the snow mobile, M = 1000 kg

Suppose initial velocity of the snow ball = u

Final velocity of snow ball and snow mobile = v = 7 cm/s

Total initial momentum, Pi = m1*u = 5*u

Total final momentum, Pf = (m1+m2)*v = (5 + 1000)*7 kg*cm/s = (1005*7) kg*cm/s

Apply conservation of momentum.

So,

Pi = Pf

=> 5*u = (1005*7) kg*cm/s

=> u = (1005*7) / 5 cm/s = 1407 cm/s = 14.07 m/s

So, snow ball's initial velocity = 14.07 m/s (Answer)

(b) In this case also, the initial momentum of the super ball is the same as the snow ball.

So, using the same principle as in part (a) -

We find that the final velocity of the snowmobile is the same as in the case (a).

Means,

m1*u = (m1 + m2)*v

=> v = m1*u / (m1+m2)

here, u = 1407 cm/s

m1 = 5 kg

m2 = 1000 kg

So,

v = (5*1407) / (5+1000) = 7 cm/s (Answer)