Speed of a Snowmobile: Snow Jump

The Physics Factbook
Edited by Glenn Elert -- Written by his students
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The Problem

animated gif

This is a mechanics problem that a physics student should be able to solve

View the clip of the snowmobile flip at killsometime.com.

In the video, a snowmobile is jumped off of an incline and flips backwards, then lands upright on the ground. Assuming that the snowmobile took off at a 45° angle and that it landed on ground at the same height as that from which it took off, you should be able to determine:

  1. Peak Altitude
  2. Range
  3. Takeoff Speed

1. Altitude

total time = frames / frame rate
total time = 36 frames / 30 frames/second = 1.2 seconds
t = 1.2 seconds / 2 = .6 seconds

y = vot + ½at2
y = (0 m/s)(.6 s) + ½(9.8 m/s2)(0.6 s)2 = 1.764 m

2. Range

vfy2 = voy2 + 2asy
0 = voy2 + 2(-9.8 m/s2)(1.764 m)
voy = (34.5744)½ = 5.88 m/s

vector diagram
x = (5.88 m/s) / (tan 45°) = 5.88 m/s

s = vxt
s = (5.88 m/s)(1.2 s) = 7.056 m

3. Take-off Speed

vector diagram

x = (5.88 m/s) / (cos 45°) = 8.32 m/s

Matthew Grabczynski -- 2005

Physics on Film pages in The Physics Factbook™ for 2005


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