Question

The $P.E.$ and $K.E.$ of a helicopter flying horizontally at a height $400m$ are in the ratio $5:2$. The velocity of helicopter is:

• A. $28m/s$
• B. $14m/s$
• C. $56m/s$
• D. $30m/s$

Answer 1

The correct option is C $56m/s$

Let mass and velocity of the helicopter be 'm' k 'v' so,

$KE=\frac{1}{2}m{v}^2$ and $PE=mgh$, where $[h=400m]$

Given ratio,

$\frac{PE}{KE}=\frac{5}{2}$

$\Rightarrow \frac{mgh}{\frac{1}{2}m{v}^2}=\frac{5}{2}\Rightarrow v^2=\frac{4}{5}gh$

$\Rightarrow v=\sqrt{\frac{4}{5}\times 10\times 400}=40\sqrt{2}\simeq 56.7m/s$