Question

Starting from rest, a 31.6 kg child rides a 8.50 kg sled down a frictionless ski slope. At the bottom of the hill, her speed is 6.4 m/s . If the slope makes an angle of 14.1° with respect to the horizontal, how far along the hill did she slide on her sled?

Answer 1

Given

Mass of the child

Mass of the sled

Total mas of child+sled system

The child+sled starts from rest, the initial speed of the child is zero

The speed of the child+sled at the bottom is

There are two forces acting on the child+sled system: Mg is the gravitational force of the Earth, N is the normal force of the ski slope on the system. The free-body diagram of the child+sled system is shown in the following figure:

The gravitational force of the Earth is resolved into components parallel and perpendicular to the ski slope. The system is not allowed to move in the direction normal to the ski slope, the net force in this direction must be zero

The equation of motion of the system in the direction parallel to the ski slope is

Substituting we get

The acceleration of the system is uniform in time. The motion of the system is governed by the kinematic's equations for uniformly accelerated motion. To find distatance traveled we use

The child slide 8.58m.