A skier leaves the ramp of a ski jump with a velocity of v = 11.0 m/s, theta = 2

Question

A skier leaves the ramp of a ski jump with a velocity of v = 11.0 m/s, theta = 26.0degree above the horizontal, as shown in the figure. The slope where she will land is inclined downward at pi = 50.0degree, and air resistance is negligible. Find the distance from the end of the ramp to where the jumper lands. Find the velocity components just before the landing. (Let the positive x direction be to the right and the positive y direction be up.) Explain how you think the results might be affected if air resistance were included?

Explanation / Answer

I will assume that the point where the skier leaves the ramp is a point on the slope I will also take this point as the (0,0) of the coordinate system being used.

vx0 = 11*cos(26)
vy0 = 11*sin(26)

x = vx0*t = 11*cos(26)*t
y = vy0*t - (1/2)*g*t^2 = 11*sin(26)*t - (1/2)*g*t^2

Now write the equation of the slope.
y = -tan(50)*x
y = -tan(50)*[11*cos(26)*t]

Equate the y values and solve for t.
-tan(50)*[11*cos(26)*t] = 11*sin(26)*t - (1/2)*g*t^2
-tan(50)*[11*cos(26)] = 11*sin(26) - (1/2)*g*t
t = 2*11*[sin(26) + tan(50)*cos(26)]/g
t = 3.39 seconds

Use t to get x and y.
x = 33.52 m
y = -39.96 m
Distance down the slope = sqrt(x^2 + y^2) = 52.16 m

A quick check gives atan(y,x) = -50 degrees so the point is on the slope

And for the velocity components at impact:
vx = constant = vx0 = 11*cos(26) = 9.89 m/s
vy = vy0 - g*t = -28.4 m/s

c) The presence of interaction with the air makes the competition more exciting. The skiers can influence the length of the jump. It would be surprising but theoretically jumps can be longer in the presence of interaction with the air! The idea is to reduce the y-component of the acceleration by using air as a source of an additional force (lift), while maintaining almost constant horizontal component of the velocity. The principle is applicable in hand gliding (when there is no air convection). Some animals also learned how to increase the range of their jumps by taking advantage of interaction with the air.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.