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Answer to Question #4823 in Mechanics | Relativity for brett

Question #4823
A daredevil jumps a canyon 12 m wide. To do
so, he drives a car up a 10 incline.
What minimum speed must he achieve to
clear the canyon?
The acceleration of gravity is 9.81 m/s2 .
Answer in units of m/s
Expert's answer
To find this, you must first find the peak altitude which occurs at
the
moment his vertical velocity is zero.
Vy(t) = Vyo -gt = 0 => t =
Vyo/g
We know the time from ground to peak altitude is equal to the
time
from peak altitude to ground. So the total time of flight is 2*t
=
2*Vyo/g.
The distance the car travels is Vxo*2*t = Vxo*2*Vyo/g = 12
meters.
Use tan10=Vyo/Vxo => Vyo = Vxo*tan10
Substitute into the
distance equation:
[2*Vxo^2*tan10]/g = 12
Vxo = sqrt[12g/2*tan10] =
sqrt[117.72 / 0.3527] = 18.27 m/s, but that
is just the horizontal
component
Vo = Vxo/cos10 = 18.55 m/s

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