Answer:
15 kg
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:
[tex]p_i=0[/tex]
The total final momentum is instead:
[tex]p_f = mv+MV[/tex]
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,
[tex]p_i = p_f\\0 = mv+MV[/tex]
Therefore, solving for M, we find the combined mass:
[tex]M=-\frac{mv}{V}=-\frac{(1)(15)}{-1}=15 kg[/tex]
