Constant Acceleration of a skier Problem

In summary, the skier travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 28 m/s. The landing falls off with a slope of 32 degrees. The skier is airborne for a total of 2.8 seconds. He goes down the incline for a total of 0.4 meters.
  • #1
bmb2009
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Homework Statement



A skier travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 28 m/s. The landing falls off with a slope of 32 degrees.
a.) How long is the skier airborne? ignoring air resistance
b.) How far down the incline does the jumper land along the incline?

Homework Equations





The Attempt at a Solution


a.) Since V_x*t=d_x I was going to find how far down the incline the skier lands then solve for two but the order of the questions makes it seem that that is how you solve part. Finding the t value first.

I wasn't really sure where to go with this but maybe finding the interesting point of the slope and the parabolic trajectory of the skier but the only information I have is the slope of the incline so I don't know how to set that up..any help?
 
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  • #2
This is a ballistics problem - I always tell people to draw the v-t diagrams.
In this case you have a bit of an issue in that the distance fallen also depends on the horizontal distance covered. You want to find where the parabola of the trajectory intersects the line of the landing.

You will end up with two equations and two unknowns - you can solve for them in either order.
 
  • #3
Simon Bridge said:
This is a ballistics problem - I always tell people to draw the v-t diagrams.
In this case you have a bit of an issue in that the distance fallen also depends on the horizontal distance covered. You want to find where the parabola of the trajectory intersects the line of the landing.

You will end up with two equations and two unknowns - you can solve for them in either order.

I understand that I need to find where they intersect but I don't know how get the equations of the parabola and the line. I have the slope of the incline but no point. And I don't know the parabola either...how do I come up with the equations?
 
  • #4
Set up a coordinate system with (x=0,y=0) the point, and t=0 the time, he leaves the track.

Questions for you to answer:
1. What is his x(t)?
2. What is his y(t)?
3.What is the relationship between x and y for the slope?

I would then solve for the x value of the impact point, from which the answers follow immediately from the above equations.
 
  • #5
ok thank you!
 

Related to Constant Acceleration of a skier Problem

What is the definition of constant acceleration?

Constant acceleration refers to a situation where an object's velocity changes by the same amount in each unit of time. This means that the object is accelerating at a constant rate.

How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the constant acceleration formula for a skier?

The constant acceleration formula for a skier is d = vi*t + 1/2*a*t^2, where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time.

How does air resistance affect the constant acceleration of a skier?

Air resistance can have a significant impact on the constant acceleration of a skier. As the skier moves through the air, air resistance creates a force in the opposite direction of motion, which can slow down the skier's acceleration. This is why skiers often try to minimize their surface area and streamline their body position to reduce air resistance and maintain a constant acceleration.

What are some real-life examples of constant acceleration for a skier?

Some real-life examples of constant acceleration for a skier include going down a ski slope, performing a jump or trick on skis, and using a ski lift to ascend a mountain. In all of these scenarios, the skier is experiencing a constant acceleration due to the force of gravity acting on them.

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