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A new ski area has opened that emphasizes the extreme nature of the skiing possible on its slopes. Suppose an ad intones "Free-fall skydiving is the greatest rush you can experience . . . but we’ll take you as close as you can get on land. When you tip your skis down the slope of our steepest runs, you can accelerate at up to 75% of the acceleration you’d experience in free fall." What angle slope could give such an acceleration?

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oladayoademosu

Answer:

48.6°

Explanation:

The forward force, F equals the component of the weight along the slope.

So mgsinθ = ma where a = acceleration and θ = angle between the slope and the horizontal.

So a = gsinθ

Since we are given that a = 75%g = 0.75g,

0.75g = gsinθ

sinθ = 0.75

θ = sin⁻¹(0.75)

= 48.6°

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