Question

Find the radius of curvature of a projectile at the highest point, fired with a velocity v, making an angle $\theta$ with the horizontal.

• A. $\frac{v^2{\sin }^2\theta }{g}$
• B. $\frac{v^2{\sin }^2\theta }{2g}$
• C. $\frac{v^2{\cos }^2\theta }{2g}$
• D. $\frac{v^2{\cos }^2\theta }{g}$

Answer 1

Answer: (D)

$\frac{v^2{\cos }^2\theta }{g}$

$a_r=\frac{v^2}{r}\Rightarrow g=\frac{{\left(vcos\theta \right)}^2}{r}\Rightarrow r=\frac{v^2{cos}^2\theta }{g}$