Find exit speed at the bottom of the ramp using kinematics only

In summary, a professional skier's initial acceleration on fresh snow is 90% of the acceleration expected on a frictionless, inclined plane, with the difference being due to friction. Due to air resistance, the skier's acceleration decreases as they pick up speed. The speed record on a mountain in Oregon is 180 kilometers per hour at the bottom of a 29.0deg slope that drops 197 m. Using kinematics equations, the exit speed of a skier in the absence of air resistance is calculated to be 62.14 m/s or 223.7 km/hr. However, the skier is not able to reach this ideal speed due to the loss caused by air resistance.
  • #1
spartan55
4
0

Homework Statement


A professional skier's initial acceleration on fresh snow is 90% of the acceleration expected on a frictionless, inclined plane, the loss being due to friction. Due to air resistance, his acceleration slowly decreases as he picks up speed. The speed record on a mountain in Oregon is 180 kilometers per hour at the bottom of a 29.0deg slope that drops 197 m. What exit speed could a skier reach in the absence of air resistance (in km/hr)? What percentage of this ideal speed is lost to air resistance?


Homework Equations


We are only on kinematics...
(v_final)^2 = (v_initial)^2 + 2*(a_parallel)*(x_final - x_initial) , where a_parallel = g*sin(29)


The Attempt at a Solution


I used trig to solve for the length of the ramp:
l*sin29 = 197
l = 406.35 m
Then I plugged this into the above kinematics equation and solved for v_final:
(v_final)^2 = 0 + 2*g*sin(29)*(406.35 - 0)
v_final = 62.14 m/s
I converted this to km/hr:
62.14 m/1s * 1km/1000m * 3600s/1hr = 223.7 km/hr, but this isn't the correct answer. I'm not sure where I went wrong.
 
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  • #2
spartan55 said:

Homework Statement


A professional skier's initial acceleration on fresh snow is 90% of the acceleration expected on a frictionless, inclined plane, the loss being due to friction. Due to air resistance, his acceleration slowly decreases as he picks up speed. The speed record on a mountain in Oregon is 180 kilometers per hour at the bottom of a 29.0deg slope that drops 197 m. What exit speed could a skier reach in the absence of air resistance (in km/hr)? What percentage of this ideal speed is lost to air resistance?


Homework Equations


We are only on kinematics...
(v_final)^2 = (v_initial)^2 + 2*(a_parallel)*(x_final - x_initial) , where a_parallel = g*sin(29)


The Attempt at a Solution


I used trig to solve for the length of the ramp:
l*sin29 = 197
l = 406.35 m
Then I plugged this into the above kinematics equation and solved for v_final:
(v_final)^2 = 0 + 2*g*sin(29)*(406.35 - 0)
v_final = 62.14 m/s
I converted this to km/hr:
62.14 m/1s * 1km/1000m * 3600s/1hr = 223.7 km/hr, but this isn't the correct answer. I'm not sure where I went wrong.
Look at the phrase in red, especially the 90%.
 
  • #3
Ahh yes that is what I forgot. Thanks Sammy!
 

FAQ: Find exit speed at the bottom of the ramp using kinematics only

1. How do you calculate the exit speed at the bottom of a ramp using kinematics?

To calculate the exit speed at the bottom of a ramp using kinematics, you will need to know the initial velocity, acceleration, and distance traveled. You can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

2. Can you use kinematics to find the exit speed at the bottom of any ramp?

Yes, kinematics can be used to find the exit speed at the bottom of any ramp as long as you have the necessary information, such as the initial velocity, acceleration, and distance traveled.

3. What other factors can affect the exit speed at the bottom of a ramp?

The exit speed at the bottom of a ramp can also be affected by the angle of the ramp, the presence of friction, and air resistance. These factors can alter the acceleration and ultimately affect the final velocity.

4. Is it important to use only kinematics to find the exit speed at the bottom of a ramp?

Using kinematics is important because it allows for a precise and accurate calculation of the exit speed. Other methods, such as using a stopwatch or measuring with a radar gun, may introduce errors and inaccuracies.

5. How can the exit speed at the bottom of a ramp be applied in real-life situations?

The exit speed at the bottom of a ramp can be applied in various real-life situations, such as calculating the speed of a car or a rollercoaster at the bottom of a hill. It can also be used in sports, like skiing or skateboarding, to determine the speed at which a person exits a ramp or jump.

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