The angle is 5x in degree with the horizontal, at which a shell be fired if at the top of its trajectory its path has a radius of curvature equal to twice the maximum height of the trajectory. Find x
Physics · Mixed Chapter
JEE Mains

Question

The angle is 5x in degree with the horizontal, at which a shell be fired if at the top of its trajectory its path has a radius of curvature equal to twice the maximum height of the trajectory. Find x

G1 Physics · Accepted Answer

Step 1: For a projectile launched at speed u and angle θ, highest-point speed is u cosθ, so radius of curvature there is R=(u²cos²θ)/g. Step 2: Maximum height above launch point is H=u²sin²θ/(2g). Step 3: Given R=2H, u²cos²θ/g=u²sin²θ/g ⇒ cos²θ=sin²θ ⇒θ=45° (usual acute projection). Step 4: θ=5x degrees, so 5x=45 and x=9. Answer: 9.