Answer to Question #4823 in Mechanics | Relativity for brett
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
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