A skier leaves the ramp of a ski jump with a velocity of v = 10.0 m/s at 0 = 15.0° above the horizontal as shown in Figure P4.49 (page 94). The slope where she will land is inclined downward at o = 50.0°, and air resistance is neg- ligible. Find (a) the distance from the end of the ramp to where the jumper lands and (b) her velocity components just before the landing. (c) Explain how you think the results might be affected if air resistance were included.
A skier leaves the ramp of a ski jump with a velocity of v = 10.0 m/s at 0 = 15.0° above the horizontal as shown in Figure P4.49 (page 94). The slope where she will land is inclined downward at o = 50.0°, and air resistance is neg- ligible. Find (a) the distance from the end of the ramp to where the jumper lands and (b) her velocity components just before the landing. (c) Explain how you think the results might be affected if air resistance were included.
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(a)
Let d denote the distance travelled by the skier along the ramp. Then, the x-distance is dcosϕ and the y-distance is –dsinϕ (downwards).
The skier’s projectile motion faces no horizontal acceleration and the gravitational acceleration (g) vertically downwards.
Their initial vertical and horizontal speeds are the sine- and cosine- components of v with respect to θ, respectively.
Solve the constant horizontal speed (vx) formula for the time (t) when the skier lands as follows:
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