Finding angle of swing?

Question

A 12kg child on a playground swing moves with a speed of 7.5m/s when the 9m long swing is at its lowest point and the acceleration of gravity is 9.8m/s^2. How can I find the angle that the swing makes with the vertical when the swing is at its highest point?

Answer 1

Use the principle of conservation of energy.

As the swing rises, all of its kinetic energy is converted into gravitational potential energy:

ΔKE = ΔPE

mv²/2 = mg(Δh)

from that you can see:

Δh = v²/(2g)

Next, use trigonometry to figure out the angle based on Δh. If you draw a diagram, you can see that:

(9m − Δh) / 9m = cos(θ)

The mass of the child is irrelevant.