In the figure, a runaway truck with failed brakes is moving downgrade at 102 km/

Question

In the figure, a runaway truck with failed brakes is moving downgrade at 102 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of theta = 11 degree. The truck's mass is 1.2 times 10^4 kg. 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.) Does the minimum length L increase, decrease, or remain the same if the truck's mass is decreased and its speed is decreased?

Explanation / Answer

step;1

given that

speed V=102 km/h=28.3 m/s

angle =11 degree

mass m=1.2*10^4 kg

step;2

now we find the minimum length to stop

V^2-u^2=2gsin(theta)*L

28.3^2=2*9.8*sin(11)*L

the minimum length L=214.5 m

step;3

the mass is decreases the length is also decreases because the mass and length directely proportional relation

the speed is decreased the length is also decreases because the velocity is directly proportional to length

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