Question

Is the statement, “The time taken by a body to reach the highest point is equal to the time taken by the body to fall from the same height” true?

Answer 1

True, the time taken by a body to reach the highest point is equal to the time taken for the body to fall from the same height.

Step 1: Time is taken by the body to rise to the highest point.

We know,

$$\begin{gathered} v=u+at \\ 0=u-gt,t=\frac{u}{g} \\ {\text{From, v}}^2{\text{-u}}^2\text{=2as} \\ 0-u^2=(-g)h,h=\frac{u^2}{2}g \end{gathered}$$

this is the maximum height.

Step 2: Time is taken by the body to fall the to ground.

$$\begin{gathered} s=ut+\frac{1}{2}a{t}^2 \\ \frac{u^2}{2}g=0+\frac{1}{2}g{t}^2 \\ {t}^2=\frac{u^2}{g^2},t=\frac{u}{g} \\ \mathrm{which}\mathrm{is}\mathrm{same}\mathrm{as}\mathrm{in}\left(1\right)\mathrm{above} \end{gathered}$$

Hence, both take the same time.