Question

If a ball is thrown vertically upwards with speed $u,$ the distance covered during the last $'t'$ seconds of its ascent is

• A. $ut$
• B. $\frac{1}{2}gt^2$
• C. $ut-\frac{1}{2}gt^2$
• D. $(u + gt )\, t$

Answer 1

Answer: (B)

$\frac{1}{2}gt^2$

Answer 2

Let time of flight be $T$ then $T = \frac{ u }{ g }$
Let $h$ be the distance covered during last 't' second of its ascent
Velocity at point $B = v _{ B }= u - g ( T - t )$
$= u - g \left(\frac{ u }{ g }- t \right)= gt$
$\Rightarrow h = v _{ B } t -\frac{1}{2} gt ^{2}$
$\Rightarrow h = gt ^{2}-\frac{1}{2} gt ^{2}=\frac{1}{2} gt ^{2}$