Question

Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. (a) If the faster stone takes 10 s to return on the ground, how long will it take the slower stone to return? (b) If the slower stone reaches a maximum height of H, how high (in terms of H) will the faster stone go? Assume the two stones are freely falling objects. 

Answer 1

(a)

$$t=2\frac{v_0}{g}$$

Hence

$$t_2=3t_1=3*10\:\rm s=30\: s$$

(b)

$$H=\frac{v_0^2}{2g}$$

Hence

$$H_2=9H_1=9H$$