How Far Does a Skier Jump at 15° Launch and 50° Slope?

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In summary, the conversation is about a skier leaving a ski jump with a velocity of 8.0 m/s and an angle of 15.0° above the horizontal. The slope is inclined at 50.0° and air resistance is negligible. The problem is to find the distance from the ramp to where the skier lands. The suggested solution involves solving for time in the y direction and substituting into the x equation to obtain a distance, using the projectile equation and substituting values for alpha, beta, v, and g.
  • #1
Jbright1406
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Homework Statement


A skier leaves the ramp of a ski jump with a velocity of v = 8.0 m/s, θ = 15.0° above the horizontal, as in the figure. The slope is inclined at 50.0°, and air resistance is negligible. (Assume up and right are positive, and down and left are negative.)

(a) Find the distance from the ramp to where the jumper lands.



Homework Equations





The Attempt at a Solution



what I am coming up with is
dcos50=(8cos15)t deltaX=Vxi(t)
-dsin50=(8sin15)t+.5(-9.8)t^2 deltaY=Vyt+.5(g)t^2

im stuck at how to solve for d and t. and i have to have this done by 11:30 :-) any helps on cracking this is more than appreciated. i think I am supposed to solve for one of them and then plug it into the other equation but I am not sure how to do that
 
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  • #2
Try solving for time in the y direction and substituting into the x equation to obtain a distance. This will involve solving a quadratic.
 
  • #3
ok, my times up anyways but i still want to figure it out. how do i solve for t in the y direction. cause in m equation i still have d right? i know the quadratic formule is x equals negative b plus or minus the sqr root of b^2-4ac all divided by 2a. i get lost there
 
  • #4
Wright the projectile equation as

y = [tan(theta)]x - g*x^2/[(Vocos(theta)]^2
Substitute x = d*cos(theta) and d*sin(theta) and solve for d.
 
  • #5
huh? i have alpha and beta. alpha is 15 beta is 50
 

Related to How Far Does a Skier Jump at 15° Launch and 50° Slope?

What factors affect a skier's jump distance?

The main factors that affect a skier's jump distance are the speed at which they approach the jump, the angle of their takeoff, the wind conditions, the snow conditions, and the skier's technique.

How is a skier's jump distance measured?

A skier's jump distance is typically measured using a tape measure or laser device that is placed at the end of the jump. The distance is measured from the takeoff point to the point where the skier lands.

What is the average distance of a skier's jump?

The average distance of a skier's jump varies depending on the level of the skier and the type of jump. However, on a standard ski jump, the average distance for a professional skier is around 120 meters for men and 90 meters for women.

How can a skier improve their jump distance?

To improve their jump distance, a skier should focus on their speed, technique, and takeoff angle. They can also work on building strength and power in their legs and core muscles, as well as practicing regularly on different types of jumps.

What are the risks of a skier's jump?

The main risks of a skier's jump include injury from a fall or crash, as well as the potential for overexertion and fatigue. It is important for skiers to have proper training and safety equipment, and to only attempt jumps that are within their skill level.

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