Question

A dog (mass 20kg) is running at 8 m/s toward a stationary skateboard (mass 2kg). When the dog reaches the skateboard, it jumps on. The dog and skateboard forward together without friction until they reach a ramp (30 degrees above horizontal). If the coefficient of kinetic friction between the ramp and the skateboard is 0.3, what is the maximum height the skateboard can reach?

Answer 1

Let us 1st calculate the combined velocity of dog and skateboard after dog jumps on it
use conservation of momentum:
m1*v1i + m2*v2i = (m1 + m2)*vf
20*8 + 2*0 = (20+2)*vf
vf = 7.27 m/s

Now use conservation of energy
Let height reached be h
Then length travelled with kinetic friction = h/sin 30= 2*h
fk = miu*m*g* cos 30 = 0.3*(20+2)*9.8*cos 30 = 56 N

Initial kinetic energy = final gravitational potantial energy + energy lost against friction
0.5*(m1+m2)*vf^2 = (m1+m2)*g*h + fk*d
0.5*(20+2)*7.27^2 = (20+2)*9.8*h + 56*2*h
581.4= 215.6*h + 112*h
h = 1.77 m
Answer: 1.77 m