Question

A particle is projected with a speed u at an angle $\theta$ to the horizontal. Find the radius of curvature at maximum height.

• A. $u^{2}co{s}^2\left(\theta \right)/g$
• B. $u^{2}co{s}^3\left(\theta \right)/g$
• C. $u^{3}co{s}^2\left(\theta \right)/g$
• D. $u^{3}co{s}^3\left(\theta \right)/g$

Answer 1

The correct option is A $u^{2}co{s}^2\left(\theta \right)/g$

At max. height $\mid v\mid =ucos\theta$

$\mid a\mid =g$

using$\mid a\mid =\frac{\mid v{\mid }^2}{R}$, where $R$ is the radius of curvature

$\frac{\mid v{\mid }^2}{R}=g$

$R=u^{2}co{s}^2\left(\theta \right)/g$