You are investing an accident in which a vehicle traveling with a horizontal velocity Vo leaves the top of a cliff of height h, and lands a horizontal distance (x) from the base of the cliff. Prove that the relationship between vo and the other variables is given by the relationship. Vo^2 = (gx^2)/(2h)

Question

You are investing an accident in which a vehicle traveling with a horizontal velocity Vo leaves the top of a cliff of height h, and lands a horizontal distance (x) from the base of the cliff. Prove that the relationship between vo and the other variables is given by the relationship. Vo^2 = (gx^2)/(2h)

Answer 1

x=Vo*t since no forces act on the car in the x direction. Solve for t, t = x/v0^2

y=Vo*t+at^2/2

in this case, y = h, Vo in the y direction is 0, a = -g and use the relationship from before.

Substitute solve for Vo^2 and your all done