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)

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} $
$\Rightarrow h = gt ^{2}-\frac{1}{2} gt ^{2}=\frac{1}{2} gt ^{2}$