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A projectile is launched with the same speed on an inclined plane — once directed down the slope and once directed up the slope. The maximum range down the slope is 3 times the maximum range up the slope. Find the angle of inclination of the plane with the horizontal.

1. 30 deg
2. 60 deg
3. 45 deg
4. none of these

Correct answer: 30 deg

Solution

Maximum range down an incline of angle alpha: R_down = v²(1+sin alpha)/(g*cos² alpha). Maximum range up: R_up = v²(1-sin alpha)/(g*cos² alpha). Ratio = (1+sin alpha)/(1-sin alpha) = 3. Solving: 1+sin alpha = 3 - 3*sin alpha => 4*sin alpha = 2 => sin alpha = 1/2 => alpha = 30 deg.

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