Question

A ball is thrown straight upward with a speed, v from a point, h meters above the ground. Show that the time taken, t for the ball to strike the ground is t= (v/g)[1+√1+(2gh/v^2)]

Answer 1

$$h(t)=h_o+v_0t-\frac {gt^2}{2}$$

$$h(t)=0$$

$$gt^2-2vt-2h=0$$

$$t=\frac {v+\sqrt {v^2+2gh}}{g}=\frac {v}{g}+\sqrt{\frac {v^2+2gh}{g^2}}$$