Register to reply

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

by spartan55
Tags: kinematics, ramp, skiing, speed, velocity
Share this thread:
spartan55
#1
Jan28-11, 08:09 PM
P: 4
1. The problem statement, all variables and given/known data
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?


2. Relevant 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)


3. 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.
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
SammyS
#2
Jan29-11, 12:58 AM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,819
Quote Quote by spartan55 View Post
1. The problem statement, all variables and given/known data
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?


2. Relevant 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)


3. 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%.
spartan55
#3
Jan29-11, 01:47 PM
P: 4
Ahh yes that is what I forgot. Thanks Sammy!


Register to reply

Related Discussions
Flow rate of a tank with RAMP at the bottom Calculus & Beyond Homework 0
Find the speed at the bottom of it's swing Introductory Physics Homework 16
2 balls, one rolling, one sliding down the same ramp. Which is faster at the bottom? Introductory Physics Homework 1
A Sphere rolling down an incline. Find the speed at the bottom Introductory Physics Homework 2
Roller Coaster, Cosine 'ramp', Exit Velocity? Introductory Physics Homework 10