A ball thrown down the Y incline strikes at a point on the incline 25 m below the horizontal as shown in the figure. If the ball rises to a maximum height of 20 m above the point of projection, the angle of projection α (with horizontal x-axis) is
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Question

A ball thrown down the Y incline strikes at a point on the incline 25 m below the horizontal as shown in the figure. If the ball rises to a maximum height of 20 m above the point of projection, the angle of projection α (with horizontal x-axis) is

Options

G1 Physics · Accepted Answer

The maximum rise above the point of projection is 20 m, so uᵧ²/(2g) = 20 and uᵧ = 20 m/s. From the figure the impact point is 25 m below the launch level, so -25 = 20t - 5t², giving t = 5 s. The horizontal displacement is 75 m, hence uₓ = 75/5 = 15 m/s. Therefore tanα = uᵧ/uₓ = 20/15 = 4/3, so α = tan⁻¹(4/3). Hence option A.