A physics professor did daredevil stunts in his spare time.His last stunt was an

Question

A physics professor did daredevil stunts in his spare time.His last stunt was an attempt to jump across a river on a motorcycle. The takeoff ramp was inclined at 53.0 degrees, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. Ignore air resistance. What should his speed have been at the top of the ramp for him to just made it to the edge of the far bank? A physics professor did daredevil stunts in his spare time.His last stunt was an attempt to jump across a river on a motorcycle. The takeoff ramp was inclined at 53.0 degrees, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. Ignore air resistance. What should his speed have been at the top of the ramp for him to just made it to the edge of the far bank?

Explanation / Answer

angle A = 53.0 degrees, sinA = 0.80, cosA = 0.60

d = 40.0 m, h = 15.0 m, H = 100 m,

find speed v

vertical displacement - h = v*sinA*t - g*t^2/2

-15 = 0.80v*t - 4.9*t^2 (1)

horizontal displacement d = v*cosA*t

= 0.60*v*t

so

v*t = d/0.60

= 40/0.60

v*t = 66.66

plug it into (1) and get

-15 = 0.80*66.66 - 4.9*t^2

t = 3.734 s

v = 66.66/t

= 66.66/3.734

v = 17.85 m/s

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