In the figure, a runaway truck with failed brakes is moving downgrade at 175 km/

Question

In the figure, a runaway truck with failed brakes is moving downgrade at 175 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of theta = 18 degree. The truck's mass is 1.5 times 10^4 kg. (a) What minimum length must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption.) Does the minimum length L increase, decrease, or remain the same if (b) the truck's mass is decreased and (c) its speed is decreased?

Explanation / Answer

given,

mass = 1.5 * 10^4 kg

angle = 18 degree

speed = 175 km/h or 48.61 m/s

by conservation of energy

initial energy = final energy

0.5 * m * v^2 = mgh

0.5 * v^2 = gh

0.5 * 48.61^2 = 9.8 * L * sin(18)

L = 390.133 m

length is dependent on the velocity not mass so,

lenagth will ramin same if truck's mass is decreased

length will be decreased if speed is decreased

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