A copy-cat daredevil trios to reenact Evel Knievel\'s 1974 attempt to jump the S

Question

A copy-cat daredevil trios to reenact Evel Knievel's 1974 attempt to jump the Snake River Canyon in a rocket-powered motorcycle. The canyon is L = 400 m wide, with the opposite rims at the same height. The height of the launch ramp at ramp rim of the canyon is h = 4 m above the rim, and the angle What is the minimum launch speed required for the daredevil to make it across the canyon? Neglect the air resistance and wind. (Express your answer to three significant figures.) Famous after his successful first jump, but still recovering from the injuries sustained in crash caused by a strong bounce upon landing, the daredevil decides to jump again but to add a landing ramp with a slope that will match the angle of his velocity at landing. It the height of the landing ramp at the opposite rim is 4 m, what is the new required launch speed? (Express your answer to three significant figures.)

Explanation / Answer

part a:

let launch speed be v m/s.

let time taken be t seconds.

then for horizonal motion:

v*cos(45)*t=400

v=565.69/t..(1)

for vertical motion:

v*sin(45)*t-0.5*9.8*t^2=-4..(2)

using v=565.69/t,

400-4.9*t^2=-4

==>t=9.08 seconds

then v=565.69/t=62.3 m/s

part b:

now vertical displacement is 0

so equation 2 becomes:

v*sin(45)*t-0.5*9.8*t^2=0

using v=565.69/t,

400-4.9*t^2=0

==>t=9.0351 seconds

then v=62.61 m/s

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