Question

Contrary to popular belief, a ski jumper does not achieve a large amount of "air" when doing a jump (less than 6 feet). This is because the ramp is almost horizontal while the landing is a steep hill. If a ski jumper leaves the hill at 26 m/s in the horizontal direction then travels 240 meters down the slope, what was the vertical distance (dy) that the ski jumper fell?

Answer 1

The vertical distance that the ski jumper fell is 417.45 m.

Step-by-step explanation:

Given;

initial horizontal velocity of the jumper,
`V_x` = 26 m/s

horizontal distance of the jumper, dx = 240 m

The time of the motion is given by;

dx = Vₓt

t = dx / Vₓ

t = 240 / 26

t = 9.23 s

The vertical distance traveled by the diver is given by;

`d_y = V_yt + (1)/(2)gt^2`

initial vertical velocity,
`V_y`, = 0

`d_y = (1)/(2)gt^2\\\\d_y = (1)/(2)(9.8)(9.23)^2\\\\d_y = 417.45 \ m`

Therefore, the vertical distance that the ski jumper fell is 417.45 m.