Question

A mango is dropped from a height h.
a. If dropped from a height of 2 h, would the
impact speed double?
b. Would the air time double when dropped from
a height of 2h ?

Answer 1

(a) The law of conservation of energy says

$$mgh=\frac{mv^2}{2}$$

The impact speed

$$v=\sqrt{2gh}\sim\sqrt{h}$$

Hence, if we dropped a mango from a height of $2h$ the impact speed increases by factor $\sqrt{2}.$

Answer: No

(b) The air time of motion

$$t=\sqrt{\frac{2h}{g}}\sim\sqrt{h}$$

Hence, if we dropped a mango from a height of $2h$ the time of motion increases by factor $\sqrt{2}.$

Answer: No