A building is being demolished with a wrecking ball. I want to cross the street where it is swinging without risking being hit.If the cable attached to wrecking ball 20 meters long do i have to cross if i start as soon as the wrecking ball and cable are straight up and down
You have half a period
T = 2 pi sqrt (L/g) = 2 pi sqrt (20/9.81)
use T/2
To determine the distance you need to cross the street without risking being hit by the swinging wrecking ball, you need to consider the length of the cable and the path of the swinging motion.
1. Start by understanding the swinging motion: The wrecking ball moves in an arc due to the swinging motion. The shape of this arc is called a pendulum.
2. Measure the length of the cable: In your case, the cable attached to the wrecking ball is 20 meters long.
3. Calculate the swinging radius: To determine the maximum distance the wrecking ball can reach from its starting point, you need to calculate the radius of the pendulum's arc. This is equal to half the length of the cable, which in this case is 10 meters (20 meters / 2).
4. Determine the width of the swinging arc: The swinging arc covers a total distance twice the radius. So, the width of the swinging arc is 20 meters (2 * 10 meters).
5. Allow for safety distance: To be on the safe side, you should add an additional distance to the width of the swinging arc. This distance will depend on the speed of the swinging motion and your level of comfort. Let's say you want to add 5 meters as an extra buffer.
6. Calculate the total distance to cross: Add the width of the swinging arc and the safety buffer to get the total distance to cross the street. In this case, it will be 20 meters (width of swinging arc) + 5 meters (safety buffer) = 25 meters.
Therefore, you need to cross a distance of at least 25 meters to safely pass the swinging wrecking ball, assuming that you start crossing as soon as the wrecking ball and cable are straight up and down.