Question

At the Winter Olympics, a ski jumper leaps from the end of the slope with a horizontal velocity of 20.5 m/s and lands 7.2 seconds later. Assuming no air resistance, (a) what was her height when she took off?

Answer 1

To calculate the height at which the ski jumper took off, we can use the equations of motion. Since there is no air resistance, we can assume that the only force acting on the ski jumper is gravity.

We can use the equation for vertical displacement:

Vertical displacement = initial vertical velocity × time + (1/2) × acceleration due to gravity × time^2

Since the ski jumper took off horizontally, her initial vertical velocity is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in these values and the given time of 7.2 seconds, we can calculate the vertical displacement.

Vertical displacement = 0 × 7.2 + (1/2) × 9.8 × (7.2)^2

Vertical displacement ≈ 0 + 1/2 × 9.8 × 51.84

Vertical displacement ≈ 252.816 meters

Therefore, the height at which the ski jumper took off is approximately 252.816 meters.