Question

A skater is moving on ice at a velocity of $15\text{m/s}$ in a circle of radius $22.5\text{m}$. What is the angle the person makes with the ground?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. $0^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Let the skater bend w.r.t vertical plane by an angle $\theta$. Then for safe skating, he should follow the condition of $\frac{v^2}{rg}=\tan \theta$
$\Rightarrow \tan \theta =\frac{v^2}{rg}$
$\Rightarrow \tan \theta =\frac{{15}^2}{22.5\times 10}=1$
$\Rightarrow \theta ={45}^{\circ }$ (This angle is with the vertical)
$\therefore$ Angle made with the ground $={90}^{\circ }-{45}^{\circ }={45}^{\circ }$