Question

An aeroplane executes a horizontal loop at a speed of 720 kmph with its wings banked at ${45}^o$. What is the radius of the loop?
Take g = 10 $m{s}^{-2}$.

• A. 4 km
• B. 4.5 km
• C. 7.2 km
• D. 2 km

Answer 1

The correct option is A 4 km

Given : $v=720$ km/h $=720\times \frac{5}{18}=200$ $m/s$

Angle of banking $\theta ={45}^o$

Radius of loop $r=\frac{v^2}{g\tan \theta }$

$\therefore$ $r=\frac{{200}^2}{10\times 1}=4000$ m $(\because \tan {45}^o=1)$

$⟹$ Radius of loop $r=4$ km