4. In 1974, Evel Knievel performed his famous Snake River Canyon stunt, where, b

Question

4. 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 56 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's trajectory as well as the initial and final velocity vectors (b) What is the minimum launch speed required for Evil Knievel to barely make it across? (c) Where does he land, if his launch speed is only half that calculated above? We neglect air resistance and any wind gusts that actually did occur) s0m oom

Explanation / Answer

given length of incline, l = 50 m

angle, theta = 56 deg

canyon width, d = 500 m

depth, d' = 180 m

a. let the point of lauch be the origin, x axis to the rgith and y axis to the top

b. minimal launch speed = v

time of flight = t

then

-l*sin(56) = v*sin(56)*t - 0.5*g*t^2

also

v*cos(56)*t = 500

hence

41.45 = v*sin(56)*500/vcos(56) - 0.5g(500/vcos(56))^2

v = 74.85682981 m/s

c. launch speed = u = v/2 = 37.42841490 m/s

range = ucos(56)*t

(-l*sin(56) - 180) = u*sin(56)*t - 0.5gt^2

-221.45 = 1.482R - 0.011197287*R^2

R = 221.60027411542 m

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