Question

If you miss a brick on the way up,during what remaining time interval can you reach out and catch the brick on its way down

Answer 1

Explanations & Calculations

• If you neglect (just for the ease of calculations) the air resistance (normally, air resistance can be easily neglected for a brick) it is a verticle motion under gravity.
• Therefore, applying $\small S = ut+\frac{1}{2}at^2$ for the brick's motion from the point it was missed & until it returns, the time interval can be found.

$\qquad \qquad \begin{aligned} \small \uparrow 0&=\small ut+\frac{1}{2}(-g)t^2\\ \small t&=\begin{cases} \small 0:\text{not apllicable}\\\\ \large\frac{2u}{g}:\small \text{applicable} \end{cases} \end{aligned}$

• Therefore depending on the speed at which it passed the catcher on its way up, this is the time available.