# Projectile Motion - Skier & Ramp

• Denize
In summary, a ski jumper acquires a speed of 119.0 km/hr by racing down a steep hill. He then lifts off into the air from a horizontal ramp. Beyond this ramp, the ground slopes downward at an angle of θ = 45 degrees.Assuming the skier is in free-fall motion after he leaves the ramp, at what distance d down the slope does the skier land?The skier covers a horizontal range of 55.74 meters down the slope after leaving the ramp.
Denize

## Homework Statement

A ski jumper acquires a speed of 119.0 km/hr by racing down a steep hill. He then lifts off into the air from a horizontal ramp. Beyond this ramp, the ground slopes downward at an angle of θ = 45 degrees.

## Homework Equations

Assuming the skier is in free-fall motion after he leaves the ramp, at what distance d down the slope does the skier land?

## The Attempt at a Solution

I converted 119.0 km/hr to m/s, so 33.055 m/s

I then try to find the horizontal range: 0=33.055^2 + 2*9.8*X and found X=55.74m
55.74cos45=78.83m down the ramp.

What have I done wrong?

Denize said:
the horizontal range: 0=33.055^2 + 2*9.8*X
That formula is for taking off and landing at the same height.
Go back to the SUVAT equations and solve from first principles.

With respect to the slope which is angled at 45 dgree, the ski jumper is jumping off the ramp with a velocity u=(119x5/18)m/s at angle of 45 degree!
Thus, the horizontal range he covers on the slope, d=(u^2xsin(2θ)/g).
Correct me if I am wrong,or you can ask for further doubts or queries.

Avimanyu Ray said:
With respect to the slope which is angled at 45 dgree, the ski jumper is jumping off the ramp with a velocity u=(119x5/18)m/s at angle of 45 degree!
Thus, the horizontal range he covers on the slope, d=(u^2xsin(2θ)/g).
Correct me if I am wrong,or you can ask for further doubts or queries.
You are wrong. Horizontal means horizontal - it doesn't mean parallel to the slope.
Gravity continues to act vertically, not orthogonally to the slope.

Avimanyu Ray
haruspex said:
You are wrong. Horizontal means horizontal - it doesn't mean parallel to the slope.
Gravity continues to act vertically, not orthogonally to the slope.
Thanks for the glitch.
Ok, suppose 'd' is the hypotenuse of an isosceles triangle of angle 45 degree and its equal sides=dcos45 or (dsin45 whatever). Then time taken for the skii jumper to cover 'd' is t=(2xh/g)½ = (2xdcos45/g)½.
Now, R=dsin45=u x t= (u^2 x 2 x dcos45/g)½
solving out the above equation will give the value of 'd'.

Avimanyu Ray said:
solving out the above equation will give the value of 'd'.
Yes it's correct now but you should let the original poster figure it out for themselves so they can learn too

Avimanyu Ray

## 1. What is projectile motion?

Projectile motion refers to the motion of an object that is launched into the air and then follows a curved path due to the force of gravity. This type of motion is characterized by two components: horizontal motion at a constant velocity and vertical motion affected by gravity.

## 2. How does the angle of the ramp affect the skier's trajectory?

The angle of the ramp affects the skier's trajectory by determining the initial velocity and direction of the skier's motion. A steeper ramp will result in a higher initial velocity and a shorter, more curved path, while a shallower ramp will result in a lower initial velocity and a longer, less curved path.

## 3. What factors affect the distance traveled by the skier?

The distance traveled by the skier is affected by several factors, including the angle of the ramp, the initial velocity of the skier, the mass of the skier, and the air resistance. These factors can all impact the trajectory of the skier and ultimately determine the distance traveled.

## 4. How does air resistance affect the motion of the skier?

Air resistance, also known as drag, acts in the opposite direction of the skier's motion and can significantly impact the trajectory and distance traveled. As the skier moves through the air, air resistance will slow them down and cause them to fall to the ground at a faster rate.

## 5. How can the equations of motion be used to analyze projectile motion?

The equations of motion, including those for displacement, velocity, and acceleration, can be used to analyze projectile motion by providing a mathematical representation of the skier's motion. By plugging in the initial conditions and known values, these equations can help determine the skier's trajectory, maximum height, and other important factors related to projectile motion.

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