Physics Open-Ended Question

Question

The slingshot ride at Great Adventure shoots people straight up vertically into the air. If the left side of the slingshot pulls on the rider with a force of 30,000 N at 30 degrees from the vertical, what angle does the right side make from the vertical if it pulls with a force of 25,000 N?

Answer 1

The vector sum of the two forces must be directed straight up.

Try to draw this picture of the vector sum:

The person is at a point A.

Towards the left at 30º from the vertical there is

a vector of length 30,000; that vector ends in a point B.

From B there is a vector of length 25,000 towards the right at an unknown angle.

That vector ends in a point C.

Let the angle at point A be α, and the angle at point C be γ.

We are given the constraints that α = 30º and that the line

AC is vertical.

The condition of AC being vertical implies that γ equals the

angle that the right side force (of 25,000 N) makes with the vertical.

Therefore we want to calculate γ.

Consider a line from B perpendicular to the side AC.

The length of that side equals ABsin(α) as well as BCsin(γ).

That is,

30000 sin(30º) = 25000 sin(γ)

γ = arcsin(sin(30º) 30000/25000) =argsin(0.6) = 36.9º