Question

A parachutist after bailing out falls $50m$ without friction. When parachute opens, it decelerates at $2m{s}^{-2}$. He reaches the ground with speed $3m{s}^{-1}$. At what height did he bail out?

($g=9.81m/s^2$)

• A. $91m$
• B. $182m$
• C. $293m$
• D. $111m$

Answer 1

The correct option is C $293m$

$\text{Initial velocity,}u=\sqrt{2gh}$

$\text{or,}u=\sqrt{2\times 9.8\times 50}=14\sqrt{5}$

$\text{The velocity at ground,}v=3\text{m/s}$

$v^2-u^2=2as$

$\text{or,}{3}^2-980=2\times (-2)\times s$

$\text{Thus,}s=\frac{971}{4},\text{which is nearly 243 m.}$

$\text{Initially he has fallen 50 m}$

$\text{Thus total height at which he bailed out}=243+50=293\text{m}$