Question

Rhoda tiller looks up to see a flowerpot fall off a ledge 9.2 m above her head. How long does she have to react and move before being hit on the head?

Answer 1

The flowerpot is in free fall, so it moves by uniformly accelerated motion with acceleration equal to $g=9.81 m/s^2$. Its initial speed is zero, so we can write the law of motion for the pot as
$S(t) = \frac{1}{2}gt^2$
where S(t) is the distance covered by the pot after a time t.
We want to find the time t at which the pot reaches ground, so the time t after which the pot has covered 9.2 m, therefore we should require S(t)=9.2 m and find t:
$9.2 m= \frac{1}{2} gt^2$
$t= \sqrt{ \frac{2 \cdot 9.2m}{9.81 m/s^2} }=1.37 s$