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

Question

A copy–cat daredevil tries 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 one rim of the canyon is h = 3 m above the rim, and the angle of the end of the ramp is 45° with the horizontal.

b)Famous after his successful first jump, but still recovering from the injuries sustained in the 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. If the height of the landing ramp at the opposite rim is 2 m, what is the new required launch speed? (Express your answer to three significant figures.)

Explanation / Answer

a. s = ut + 0.5at² vertically: -6.95 = (u sin(45))t + 0.5(-9.8)t² horizontally: 432.9 = (u cos(45))t t = 432.9/(u cos(45)) -6.95 = (u sin(45))(432.9/(u cos(45))) - 4.9(432.9/(u cos(45)))² -6.95 = 432.9 - 918271.8/(u² (0.5)) -219.925u² = - 918271.8 u² = 4175.386... u = 64.617... minimum launch speed = 64.6 m/s (3sf) b. s = ut + 0.5at² vertically: -4.02 = (u sin(45))t + 0.5(-9.8)t² horizontally: 432.9 = (u cos(45))t t = 432.9/(u cos(45)) -4.02 = (u sin(45))(432.9/(u cos(45))) - 4.9(432.9/(u cos(45)))² -4.02 = 432.9 - 918271.8/(u² (0.5)) -218.46u² = - 918271.8 u² = 4203.386... u = 64.833... minimum launch speed = 64.8 m/s (3sf)

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