Achild on a playground swings through a total of 32 degrees. if the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?

A = y/cos32

That is the amplitude A in terms of the displacement y.

Explanation: Since the displacement in the question In the question is the same in both direction, it is a Simple Harmonic Motion problem. In s.h.m the amplitude of displacement A is related to the displacement itself y by this simple equation

y = A* cos(theta)

So, A = y/cos(theta)

A = y/cos32.

If the magnitude of the displacement y is given, you just substitute in.

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

the total distance traveled by the car is

30km + 49km = 79 km .