Question

A student is standing on the roof of a school (20m) throwing water balloons downward with a velocity of 5m/s .
How long will it take the ballon to reach the ground ?
What will be the velocity of the ballon right before it hits the ground ?

Answer 1

The velocity of the balloon right before it hits the ground is

$$v_f=\sqrt{v_i^2+2gh}=20\text{ m/s}.$$

The time it will take can be found from the equation for displacement:

$$h=v_it+\frac{gt^2}{2},\\\space\\ t^2\cdot\frac{g}2+t\cdot v_i-h=0$$

is a simple quadratic equation. The solution is

$$t=\frac{-v_i\pm\sqrt{v_i^2+2gh}}{g}=\big|^{-2.6\text{ s}}_{\space\space\space1.6\text{ s}}$$

Of course, only 1.6 s is a correct root.