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tentoes
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Problem: A motorcyclist is about to jump across a river. The takeoff ramp is inclined at 53 degrees above the horizontal, the river is 40.0m wide, and the far bank is 15.0m lower than the top of the ramp. Ignore air resistance. What must the motorcyclist's speed be at the top of the ramp in order to just make it to the edge of the far bank?
So I know that in the x-direction: a=0, v=initial velocity * cos(53), position=Vi*cos(53)*t
and in the y direction: a=-9.8, V=-9.8*t+Vi*sin(53), position = -4.8t^2+Vi*sin(53)+15 (if "origin" here is (0, 15).So I'm missing time and initial velocity, but the equation for velocity in the x direction doesn't have t in it, so I know V=40/t, and so Vi=40/(t*cos(53)). Then I can plug that equation in for Vi in the y-position equation and solve for t (so I have t= √(((40*sin(53)/cos(53))+15)/4.8) so t=3.77 seconds, and plug that value into either velocity equation, and I get 10.61m/s. Only problem is, this is the wrong answer, and the correct one is 17.8m/s - so where am I going wrong here? I've looked at a couple of explanations of this problem not involving an overall change in y and I understand why this should work, but I've redone and gone over the problem multiple times now and there is no 17.8m/s to be found!
so I have t= √(((40*sin(53)/cos(53))+15)/4.8
So I know that in the x-direction: a=0, v=initial velocity * cos(53), position=Vi*cos(53)*t
and in the y direction: a=-9.8, V=-9.8*t+Vi*sin(53), position = -4.8t^2+Vi*sin(53)+15 (if "origin" here is (0, 15).So I'm missing time and initial velocity, but the equation for velocity in the x direction doesn't have t in it, so I know V=40/t, and so Vi=40/(t*cos(53)). Then I can plug that equation in for Vi in the y-position equation and solve for t (so I have t= √(((40*sin(53)/cos(53))+15)/4.8) so t=3.77 seconds, and plug that value into either velocity equation, and I get 10.61m/s. Only problem is, this is the wrong answer, and the correct one is 17.8m/s - so where am I going wrong here? I've looked at a couple of explanations of this problem not involving an overall change in y and I understand why this should work, but I've redone and gone over the problem multiple times now and there is no 17.8m/s to be found!
so I have t= √(((40*sin(53)/cos(53))+15)/4.8
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