Question

A stone projected at angle $\theta$ with horizontal from the roof of a tall building falls on the ground after three second. Two second after the projection it was again at the level of projection. Then the height of the building is $(g=10{\text{m/s}}^2)$

• A. $5\text{m}$
• B. $25\text{m}$
• C. $20\text{m}$
• D. $15\text{m}$

Answer 1

The correct option is D $15\text{m}$


Time of flight of the stone to reach same level of projection $=2\text{s}$
$\Rightarrow \text{Time of flight}=T=\frac{2u\sin \theta }{g}=2\text{s}$
$\Rightarrow u\sin \theta =10\text{m/s}$
When the stone reaches ground, its displacement in the vertical direction from the point of projection $=-H$ (taking downward direction as negative)
Using second equation of motion in the vertical direction, we get $-H=u\sin \theta t–\frac{1}{2}g{t}^2$
$-H=10\left(3\right)-5(3{)}^2\Rightarrow H=15\text{m}$
$\therefore$ Height of the building $=15\text{m}$