question_answer

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)  \[(u+gt)t\]

Correct Answer: B

Solution :

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 \[B={{v}_{B}}=u-g(T-t)\]             \[=u-g\left( \frac{u}{g}-t \right)=gt\] \[\Rightarrow \]               \[h={{v}_{B}}t-\frac{1}{2}g{{t}^{2}}\] \[\Rightarrow \]               \[h=g{{t}^{2}}-\frac{1}{2}g{{t}^{2}}=\frac{1}{2}g{{t}^{2}}\]