Evil Kneivel is jumping the Caesar Evil Kneivel is jumping the Caesar\'s Palace

Question

Evil Kneivel is jumping the Caesar

Evil Kneivel is jumping the Caesar's Palace fountain in a 1982 Lincoln Continental. The car has a launching velocity of 60 miles per hour as it hits the front of the ramp when the engine dies (just before going up the ramp). Realizing he is in trouble, he hits his brakes and skids for the last 30 feet of the ramp. The concrete ramp is inclined at 37 degrees from the horizontal and has a length (how far the car travels) of 40 feet. He misses his landing ramp and the car plummets headlong into a balcony that is 25 feet above ground level. You can estimate the work done by plastic deformation as: W= C u, where C is the crush factor and u is the amount of deformation. Assume negligible air resistance. Assuming he lives if the car deforms less than 4 feet, does he survive? Please show work.

Explanation / Answer

60 miles/hr = 88 ft/s

Normal force on car = mg*cos37 = 5360*32.2*sin37 = 103868.46 lb-ft/s^2

Friction force = 0.7*103868.46 = 72707.9 lb-ft/s^2

Work done by friction = 72707.9*30 = 2181237.6 lb-ft^2/s^2

Energy conservation between locations 1 and 3:

1/2*m*v1^2 = mg*h3 + 1/2*m*v3^2 + Work done by Fric

1/2*5360*88^2 = 5360*32.2*24.07 + 1/2*5360*v3^2 + 2181237.6

v3 = 73.35 ft/s

Energy conservation between 3 and 4:

1/2*m*v3^2 + mg*h3 = 1/2*m*v4^2 + mg*h4

1/2*5360*73.35^2 + 5360*32.2*24.07 = 1/2*5360*v4^2 + 5360*32.2*25

v4 = 72.94 ft/s

KE at 4 is 1/2*(5360/32.2)*72.94^2 = 442791.4 lb-ft

W = Cu

C = 7384 lb-ft/in

442791.4 = 7384*u

u = 60 in = 5 feet

He does not survive!

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