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A particle is projected from the ground with some initial velocity. Its trajectory is given by y = 8x - 2x². If the initial angle of projection with the horizontal is arctan(k), find k.

1. 4
2. 6
3. 8
4. 10

Correct answer: 8

Solution

The trajectory equation is y = 8x - 2x². The slope at the launch point (x=0) equals tan(theta): dy/dx|_(x=0) = 8 - 4*0 = 8. Therefore the angle of projection satisfies tan(theta) = 8, so k = 8.

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