SOLUTION: MOTORCYCLE JUMP: The range of a projectile is directly proportional to the square of its velocity. If a motorcyclist can make a jump of 140 feet by coming off a ramp at 60mph, fin

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Question 288732: MOTORCYCLE JUMP:
The range of a projectile is directly proportional to the square of its velocity. If a motorcyclist can make a jump of 140 feet by coming off a ramp at 60mph, find the distance the motorcyclist could expect to jump if the speed coming off the ramp were increased to 65mph. Round to the nearest tenth of a foot.
I have 12 problems similar to this but don't quite understand how to get the answer (no answer key to double-tap correctness or incorrectness). Could someone please explain the formula to me, or what I should do to determine the solution? An answer is nice, but understanding the formula is necessary to finish the rest of the problems. Any help offered is greatly appreciated! Thank you :D
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
If the Range is directly proportional to the square of the velocity, you can set up an equation like this:

R=av%5E2

where R=range, a=proportionality constant, and v=velocity

140=a%2860%29%5E2
a=7%2F180

Now use this value of a with the new information, that v=65mph to solve for R:

R=%287%2F180%29%2865%29%5E2
R=164.3

The range would be 164.3 feet if the speed was increased to 65mph.

Hope this helps. Please let me know if you have any questions.