Question

An aircraft executes a horizontal loop with a speed of $150\text{m/s}$ with it's wings banked at an angle of ${12}^{\circ }$. The radius of the loop is $(g=10{\text{m/s}}^2,\tan {12}^{\circ }=0.21)$

• A. $10.7\text{km}$
• B. $9.6\text{km}$
• C. $7.4\text{km}$
• D. $5.8\text{km}$

Answer 1

The correct option is A $10.7\text{km}$

Using the relation for the radius $\left(r\right)$ of loop
$\text{tan}\theta =\frac{v^2}{rg}$
$\text{or tan}{12}^{\circ }=\frac{(150{)}^2}{r\times 10}$
or $r=\frac{2250}{0.21}=10.7\times {10}^3\text{m}=10.7\text{km}.$