Question

A girl swings back and forth on a swing with ropes that are 4.00m long. The maximum height she reaches is 2.10m above the ground. At the lowest point of the swing, she is 0.500m above the ground.

What is the girl

Answer 1

Energy is conserved here. So when she swings forward or back, she gains gravitational potential energy, because she increases in height, and in return she loses kinetic energy. That is why she eventually stops moving forward or back and returns the opposite direction. The fastest point in her swing will ALWAYS be the bottom of the swing, this is when she has "no" gravitational potential energy and everything is in kinetic.

So the two energies are:

Pe = Ke
mgh = (1/2) * m * v^2

Notice her mass doesn't matter because it cancels out from both sides of the equation. That is why they didn't give it to you.

The height she achieves from lowest to highest point is 2.1 - .5 = 1.6m. So,

9.8 * 1.6 = (1/2)* v^2

v = sqrt(2*9.8*1.6) = 5.6 m/s

You can do this some way with the length of the rope, but I can't remember exactly what it is. Your best bet is to just use conservation of energy equations for EVERYTHING. They ALWAYS work and they are way less terms than anything else.