# ¤While jumping for a bird your cat falls off your apartment building 45 meters high (but lands in a soft pile of marshmallows of course). ¤1) How long did it take to fall? ¤2) How fast is he going when he reaches the bottom?

## I dont remember which formulas were used for how long something falls and for speed.

Mar 16, 2017

A....pile of marshmallows....!

#### Explanation:

I would suppose the vertical (downwards) initial velocity of the cat equal to zero (${v}_{i} = 0$); we can start using our general relationship:
${v}_{f}^{2} = {v}_{i}^{2} + 2 a \left({y}_{f} - {y}_{i}\right)$
where $a = g$ is the acceleration of gravity (downwards) and $y$ is the the height:
we get:
${v}_{f}^{2} = 0 - 2 \cdot 9.8 \left(0 - 45\right)$
${v}_{f} = \sqrt{2 \cdot 9.8 \cdot 45} = 29.7 \frac{m}{s}$
This will be the velocity of "impact" of the cat.

Next we can use:
${v}_{f} = {v}_{i} + a t$
where ${v}_{f} = 29.7 \frac{m}{s}$ is directed downwards as the acceleration of gravity so we get:
$- 29.7 = 0 - 9.8 t$
$t = \frac{29.7}{9.8} = 3 s$