An inclined plane makes an angle 30° above the horizontal. A projectile is fired from a point on the plane with speed 10√7 m/s and strikes the inclined plane again with horizontal velocity. Neglect air resistance and take g = 10 m/s². The range measured along the inclined plane is:
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Question

An inclined plane makes an angle 30° above the horizontal. A projectile is fired from a point on the plane with speed 10√7 m/s and strikes the inclined plane again with horizontal velocity. Neglect air resistance and take g = 10 m/s². The range measured along the inclined plane is:

Options

G1 Physics · Accepted Answer

For horizontal impact, tanθ = 2tanα. With α = 30°, tanθ = 2/√3, so sinθ = 2/√7 and cosθ = √3/√7. Also sin(θ - 30°) = sinθ cos30° - cosθ sin30° = (2/√7)(√3/2) - (√3/√7)(1/2) = √3/(2√7). The inclined range is R = [2u²cosθ sin(θ - α)]/[g cos²α]. Substituting u² = 700, cosθ = √3/√7, sin(θ - α) = √3/(2√7), cos²30° = 3 4 \frac{3}{4} 4 3 ​ gives R = 40 m. Therefore option C is correct.