Question

A body is projected vertically upward with a velocity u. If it passes through a certain point during its upward motion after time t, then it will pass through the same point during its return journey further after time t in (Take G as acceleration due to gravity)

• A. $\frac{2u}{g}$
• B. $2[\frac{u}{g}+t]$
• C. $[\frac{u}{g}-t]$
• D. $2[\frac{u}{g}-t]$

Answer 1

The correct option is D $2[\frac{u}{g}-t]$

Time taken by the body for motion from A to B= t

Now let time taken by the body for motion from A to C= T

and let time taken by the body for motion from B to C=t'

From equation of motion, we can write

v=u+at

$\Rightarrow$0=u-gT

$\Rightarrow$T=$\frac{u}{g}$

Since, T=t+t'

So, t'=T-t

$\Rightarrow$t'=$\frac{u}{g}$-t

So, now time taken for journey from B to C and again from C to B is 2t'=$2(\frac{u}{g}-t)$