Wrecking ball and time question-please help!

Question

A building is being knocked down with a wrecking ball, which is a big metal sphere that swings on a 13-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.

1. How much time do you have to move out of the way?

Answer 1

The wrecking ball on the cable constitutes a pendulum. The formula for the period (time for one complete oscillation) is T = 2π √ L/g where L = cable length and g is 9.8 m/s^2 and T is in seconds (this holds best for angles of deviation from vertical of about 15°).

If the person is standing directly beneath the point of where the ball is hanging before being elevated for the swing, this is about ¼ T, so finding T and dividing by 4 will give you the time before it hits the person.

T = 2π √ 13 m / 9.8 m/s^2 = 7.2 s for one complete cycle, so the answer is 7.2/4 = 1.8 s.

Always check the math.