After a short time, the moving sled with the child aboard reached a rough level surface that exerts a constant frictional force of 54 Newtons on the sled. How much work must be done by friction to bring the sled with the child to a stop

Wf = –750J

Explanation:

The full solution can be found in the attachment below.

This problem involves the concepts of conservation of momentum and energy.

The potential energy of the sled and child combined is constant since thehy are moving in a level surface.

To find the initial velocity of the sled with child we use the principle of momentum conservation to calculate the v1 which is the commovelocity of the child and sled.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west