Question

A building is being knocked down with a wrecking ball, which is a big metal sphere that swings on a 10-m-long cable. You are (unwisely!) standing directly beneath the point from which the wrecking ball is hung when you notice that the ball has just been released and is swinging directly toward you. How much time do you have to move out of the way?

Answer 1

t = 1.59 s

Step-by-step explanation:

This system can be approximated as a pendulum, in this case the ball is much heavier than the cable, so we can neglect its weight, in addition this metal cable is inextensible, so this is a simple pendulum, which has speed angular

w = √g/L

Angular velocity is related to frequency and period.

w = 2π f

f = 1 / T

w = 2π / T

2π / T = √g / L

T = 2π √L/g

Let's calculate

T = 2π √ (10 / 9.8)

T = 6.35 s

Let's analyze the period is the time of a complete swing, the person is at the lowest point of the swing that corresponds to ¼ of the swing

t = ¼ T

t = ¼ 6.35

t = 1.59 s

This is the time the person has to move