In 1974, Evel Knievel performed his famous Snake River Canyon stunt, where, by m
ID: 2121177 • Letter: I
Question
In 1974, Evel Knievel performed his famous Snake River Canyon stunt, where, by means of a steam-powered rocket, the X-2 Skycycle, he accelerated up a 56o inclined ramp that was 50m long (along the incline), and then shot across the canyon, attempting to reach the far rim. If the width of the canyon is 500m and the depth 180m, and we assume that both rims are at the same height with respect to the bottom of the canyon:
a) Draw an x-y coordinate system containing all given information, the rider%u2019s trajectory, as well as the initial and final velocity vectors.
(b) What is the minimum launch speed required for Evel Knievel to barely make it across?
(c) Where did he land, if his launch speed was only half that calculated above? We neglect air resistance and any wind gusts (that actually did occur).
Explanation / Answer
a)
(a)
Inital velocity, u = uxi + uyj;
Final velocity, v = vxi + vyj;
Horizontal displacement = 500 m;
Vertical displacement = -50m;
ux = u*cos(56) = u*0.559
uy = u*sin(56) = u*0.829
ax = 0 m/s2, ay = -g = -9.81 m/s2;
Let t be the time of flight;
sx = ux*t + 0.5*ax*t2;
or, 500 = (u*t)*0.559;
or, u*t = 500/0.559........(1)
sy = uy*t + 0.5*ay*t2;
or, -50 = (u*t)*0.829 - 0.5*9.81*t2;
from eqn (1),
solve u and t
or t =
so, u =
Hence minimum lanuch speed =