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A particle is projected from the foot of a fixed inclined plane whose…

Question

A particle is projected from the foot of a fixed inclined plane whose surface makes 30 degrees with the horizontal. The launch speed is 20 m/s and the direction of projection can be chosen freely (in the vertical plane containing the line of greatest slope). Taking g = 10 m/s^2, find the maximum possible range measured along the inclined surface, up the incline (in metres). Give the answer to two decimal places.

✓ Verified answer: 26.67checked by our engine — not a guess

Step-by-step solution

For projection up a plane of inclination alpha, the range along the incline is maximised when the launch direction bisects the angle between the incline and the vertical.

The maximum range is R_max = v^2 / [g (1 + sin alpha)].
With v = 20, g = 10, alpha = 30 deg (sin = 1/2): R_max = 400 / [10 (1 + 0.5)] = 400/15 = 26.6667 m, i.e.

26.67 m.

Final answer26.67

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