Question

A body is projected upwards with a velocity $u$. It passes through a certain point above the ground after time $t_1$. The time after which the body passes through the same point during the return journey is

• A. $(\frac{u}{g}-t_1^2)$
• B. $2(\frac{u}{g}-t_1)$
• C. $3(\frac{u^2}{g}-t_1)$
• D. $3(\frac{u^2}{g^2}-t_1)$

Answer 1

The correct option is B $2(\frac{u}{g}-t_1)$


Here, $|v_A|=|v_B|$
$v_A=u-g{t}_1....\left(1\right)$
$-v_B=u-g{t}_2\Rightarrow -v_A=u-g{t}_2.....\left(2\right)$
By adding $\left(1\right)$ and $\left(2\right)$, we get
$0=2u-g(t_1+t_2)$
$2u=g(t_1+t_2)$
$t_1+t_2=\frac{2u}{g}$
$t_2=\frac{2u}{g}-t_1$

The time after which it passes the same point $=t_2-t_1$
$=\frac{2u}{g}-t_1-t_1=\frac{2u}{g}-2t_1\Rightarrow 2(\frac{u}{g}-t_1)$