Question

A body projected from the ground reaches a point $X$ in its path after $3$ seconds and from there it reaches the ground after further $6$ seconds. The vertical distance of the point $X$ from the ground is (acceleration due to gravity $=10\, ms ^{-2}$ )

• A. 30 m
• B. 60 m
• C. 80 m
• D. 90 m

Answer 1

Answer: (D)

Given, acceleration due to gravity
$(g)=10\, ms ^{-2}$
According to the question, Total time of flight $(t)=\frac{2 u}{g}$
where, $u$ is initial vertical velocity.
or, $9=\frac{2 u}{g} $ or,$u=\frac{9 g}{2}$
or, $u=\frac{9 \times 10}{2}$ or, $u=45\, m / s$
Since, in covering the vertical distance, $g$ becomes negative,
$\Rightarrow h=u t-\frac{1}{2} g t^{2}$
Or, $h=45 \times(3)-\frac{1}{2} \times 10 \times(3)^{2}$
Or, $h=135-45$
Or, $ h=90 \,m$