Question

A child of mass 50 kg is on a swing which is suspended by 4.0m ropes from a rigid support. The horizontal speed of the swing as it passes through the lowest point is 3.0 ms^-1.

What is the angle θ that the ropes make with the vertical when the swing is at the highest point?

Answer

We take the lowest point as the reference to measure the height of the child as he swings.

Since the lowest point is the reference level, the gravitational potential energy is 0 at the lowest point. As the child swings from the lowest point to the highest point, kinetic energy is converted to gravitational potential energy.

Using the value of h, we can find the length of the sides of the triangle.