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. $\frac{1}{2}g{t}^2$
• C. $ut-\frac{1}{2}g{t}^2$
• 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 $B=V_B=u-g(T-t)$
$=u-g\left(\frac{u}{g}-t\right)=gt$
$\Rightarrow h=V_{B}t-\frac{1}{2}g{t}^2$
$\Rightarrow h=g{t}^2-\frac{1}{2}g{t}^2=\frac{1}{2}g{t}^2$