A projectile is fired with fixed speed u from a point on an inclined plane that makes an angle α above the horizontal. If θ is the angle of projection measured from the horizontal, the range measured along the inclined plane is maximum when:
Options

Question

A projectile is fired with fixed speed u from a point on an inclined plane that makes an angle α above the horizontal. If θ is the angle of projection measured from the horizontal, the range measured along the inclined plane is maximum when:

Options

G1 Physics · Accepted Answer

The range along the incline is R = [2u²cosθ sin(θ - α)]/[g cos²α]. Using 2cosθ sin(θ - α) = sin(2θ - α) - sinα, we get R = [u²{sin(2θ - α) - sinα}]/[g cos²α]. For fixed u and α, R is maximum when sin(2θ - α) = 1. Thus 2θ - α = 90°, giving θ = 45° + α/2. Therefore option C is correct.