What Is the Distance a Skier Lands From a Ramp?

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In summary, a skier with a velocity of 10.0 m/s and an angle of 15.0° above the horizontal leaves a ramp in a ski jump. The slope is inclined at 50.0° and air resistance is negligible. Using equations for distance and time, the distance from the ramp to where the jumper lands can be calculated. However, initial calculations were incorrect due to not considering the negative value of Yf. Correcting this yields a final time of 2.88 seconds for the jumper to reach the landing point.
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Homework Statement


A skier leaves the ramp of a ski jump with a velocity of 10.0 m/s, 15.0° above the horizontal, as shown in Figure P3.57. The slope is inclined at 50.0°, and air resistance is negligible. Find the distance from the ramp to where the jumper lands .
image092020141179.png

Homework Equations


tan50degrees=Yf/Xf
Yf = Yi + Vyi(t) + .5(ay)t2
Xf=Xi+Vx(t)

The Attempt at a Solution


Plugging in numbers into the first second equation using the first equation and solving for distances gave me the following: Xf(tan50) = 2.59t + -4.9t2 . Then I solved for the third equation and resulted in Xf=9.66t. Plugging this into the partially solved second equation yielded: 9.66tan(50)t = 2.59t - 4.9t2 which simplifies to -4.9t2 - 8.91t. t is supposed to equal 2.88 seconds but my solution doesn't yield that at all. What am I doing wrong? Thanks.
 
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got it... the Yf i used was not negative.
 

FAQ: What Is the Distance a Skier Lands From a Ramp?

What is a "Two-Dimensional Motion Problem"?

A "Two-Dimensional Motion Problem" is a type of physics problem that involves the motion of an object in two dimensions, typically in the x and y directions. This means that the object is moving not only horizontally but also vertically.

What is the difference between one-dimensional and two-dimensional motion?

The main difference between one-dimensional and two-dimensional motion is the number of directions in which the object is moving. In one-dimensional motion, the object only moves along a single axis, while in two-dimensional motion, the object can move along two axes simultaneously.

How do you solve a "Two-Dimensional Motion Problem"?

To solve a "Two-Dimensional Motion Problem", you need to break down the motion into its x and y components. This can be done using trigonometry and vector addition. Once you have the components, you can use equations of motion and kinematic equations to solve for the unknown variables.

What are some common examples of "Two-Dimensional Motion Problems"?

Some common examples of "Two-Dimensional Motion Problems" include projectile motion, circular motion, and motion on an inclined plane. These types of problems can be seen in real-life scenarios such as a ball being thrown, a car moving along a curved road, or an object sliding down a ramp.

Why is understanding "Two-Dimensional Motion Problems" important in science?

Understanding "Two-Dimensional Motion Problems" is important in science because many physical phenomena involve motion in more than one direction. By learning how to solve these types of problems, scientists can better understand and predict the behavior of objects in the real world, and make accurate calculations for experiments and engineering designs.

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