Question

Trapper stands on a skateboard at rest and throws a 1 kg rock at a velocity of 15 m/s. Trapper moves back at 1 m/s. What is the combined mass of Trapper and the skateboard?

Answer 1

15 kg

Step-by-step explanation:

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the (Trapper+skateboard) + rock system must be conserved.

At the beginning, the total momentum of the system is zero, since they are at rest:

`p_i=0`

The total final momentum is instead:

`p_f = mv+MV`

where:

m = 1 kg is the mass of the rock

v = 15 m/s is the velocity at which the rock is thrown

M is the total combined mass of Trapper and the skateboard

V = -1 m/s is the recoil velocity of Trapper and the skateboard (they move in the opposite direction to the rock)

Since the total momentum is conserved,

`p_i = p_f\\0 = mv+MV`

Therefore, solving for M, we find the combined mass:

`M=-(mv)/(V)=-((1)(15))/(-1)=15 kg`