A well-engineered ski jump is less dangerous than it looks because skiers hit th

Question

A well-engineered ski jump is less dangerous than it looks because skiers hit the ground with very small velocity components perpendicular to the ground. Skiers leave the Olympic ski jump in Lake Placid, New York, at 30 m/s at an angle of 9.5 degrees below the horizontal. Their landing zone is a horizontal distance of 55 m from the end of the jump. The ground at that point is contoured so skiers' trajectories make an angle of only 3.0 degrees with the ground on landing,
What is the slope of the ground in the landing zone?

Explanation / Answer

Time taken to land = 55/30cos9.5 = 50/29.588 = 1.85seconds Net component of vertical velocity = 30sin9.5 + 9.8*1.85 = 23.08m/s angle made by net velocity with horizontal = tan^-1 (23.08/29.588) = 37.95degrees angle made by the ground in the landing zone = 34.95degrees. Slope = tan(34.95) = 0.7

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