Question

A jet plane flying at a constant velocity v at a $\text{height}=8\text{km}$ is tracked by a radar R located at O directly below the line of flight. If angle $\theta$ is decreasing at rate of $0.025\text{rad/s}$, the velocity of plane when $\theta ={60}^{\circ }$ is

• A.
  1440 km/h
• B.
  960 km/h
• C.
  1920 km/h
• D.
  480 km/h

Answer 1

The correct option is B

960 km/h
$tan\theta =\frac{h}{x}\Rightarrow xtan\theta =h\Rightarrow cot\theta =\frac{x}{h}$
Now, since $v=\frac{dx}{dt}$
$\Rightarrow v=h\times cose{c}^2\theta \times \frac{d\theta }{dt}$
$v=\frac{8\times 4}{3}\times 0.025\times 60\times 60\text{km/h}$
$\Rightarrow v=960\text{km/h}$