How to work out momentum after a dog jumps onto a skateboard?

Momentum and velocity are vectors. This means they have magnitude and direction. I always say the direction of the first object’s velocity is the positive. Since the skateboard is going in the opposite direction, its velocity is negative. Let’s determine the initial momentums.

For dog, M = 10 * 4.5= 45
For the skate board, M = 4 * -7 = -28
Total initial momentum = 45 + -28 = 17
Since the dog is on the skateboard, the total mass is the sum of the two masses.

Total mass = 8.5 kg
Final momentum = 8.5 * v
Since momentum is always conserved, the final and initial momentums are equal.

8.5 * v = 17
v = 2 m/s
I hope this helps you to understand how to solve this type of problem.

1

So we have before mounting Mv - mV = (M + m)u after. You can find u = (10*4.5 - 4*7)/(14) = 1.21 in the direction the dog was going (plus).

So the momentum P = 14*1.21 = 16.9 kg.m/s ANS.

NOTE: = 10*4.5 - 4*7 =1.700E+01 kg.m/s which confirms the conservation of momentum law.