Question

A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Figure 1). The takeoff ramp was inclined at 53.0∘
, the river was 40.0 m
wide, and the far bank was 15.0 m
lower than the top of the ramp. The river itself was 100 m
below the ramp. You can ignore air resistance.

Answer 1

First, let's analyze the horizontal motion. We want to find the velocity at takeoff, which we'll call v0x. We can use the equation:

v0x = v0 * cos(theta)= cos 53 * v0 = 0.6 v0
t = time to cross = 40 meters / (0.6 v0) =66.7 v0 which is also the time in the air
Next, let's analyze the vertical motion. We want to find the time it takes for the motorcycle to reach the other side of the river. We can use the equation:

h = h0 + v0y * t + (1/2) * g * t^2
-15 = v0y * t - (1/2) * g * t^2 (note - sign)
but v0y = v0 sin 53 = 0.8 v0
-15 = .8 v0 t - (1/2 g t^2)
but we know t = 66.7 v0
so
-15 = .8 (66.7 v0^2) - 4.9 (66.7^2) V0^2) = 53.4 v0^2 - 4449 v0^2 = - 4395 v0^2
v0 = 0.058 m/s