Question

In Fig, a runaway truck with failed brakes is moving downgrade at 160 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of è = 11°. The truck's mass is 1.5 x 104 kg. (a) What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption.) What is the minimum length L if (b) the truck's mass is decreased by 11% and (c) its speed is decreased by 11%?

Answer 1

The truck rises a distance of L sin 11, before momentarily stopping. At that point,
M g L sin 11 = (1/2) M Vo^2, where Vo is the initial velocity

Thus L = Vo^2/(2 g sin 11

For b, you will get the same answer, since M cancels out.

For (c), multiply the length required by (0.89)^2 = 0.792

Friction is being neglected. Often a gravel surface is used on esacape ramps to increase friction. The rotational kinetic energy of the wheels is also being neglected.

Answer 2

If The Angle is 11degree then we can use inclined plane equation
a=gsin0-f/m....1
by using 1st law of motion we have:
vf=vi+at.....2