Question

A body is projected from the ground at an angle of ${60}^o$ to the horizontal with a speed $20m/s$. the radius of the curvature of the path of the particle when its velocity makes an angle of ${30}^o$ to the horizontal.

• A. $12.6m$
• B. $14.3m$
• C. $17.3m$
• D. $15.4m$

Answer 1

The correct option is C $17.3m$

Radius of curvature $r=\frac{R}{2}$ where R is the range

$r=\frac{R}{2}=\frac{u^2\sin 2\theta }{2g}$ where 'u' is initial speed

$r=\frac{{20}^2\times \sin 2\left({30}^{\circ }\right)}{2\times 10}$

$=\frac{400\times \frac{\sqrt{3}}{2}}{20}$

$=10\sqrt{3}=17.3m$