Answer to Question #172240 in Physics for tine

Question #172240

Two balls are dropped to the ground from different heights. One is dropped after the other, but they both strike the ground at the same time, 0.5 sec. after the first was dropped. What is the difference in the heights from which they were dropped?

Expert's answer

"H=\\frac{gt_0^2}{2}"

"h=\\frac{gt^2}{2}"

"H-h=\\frac{gt_0^2}{2}-\\frac{gt^2}{2}=\\frac{g}{2}(t_0^2-t^2)=\\frac{g}{2}(t_0^2-(t_0-\\Delta t)^2)"

The difference in height will depend on the time between throws of balls. There is not enough data in the problem to find it. Therefore, the problem does not have an unambiguous solution.

If "\\Delta t=0.2\\ s" then "H-h=0.784\\ m"

If "\\Delta t=0.4\\ s" then "H-h=1.176\\ m"