In the figure, a runaway truck with failed brakes is moving downgrade at 172 km/

Question

In the figure, a runaway truck with failed brakes is moving downgrade at 172 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of ? = 15

In the figure, a runaway truck with failed brakes is moving downgrade at 172 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of ? = 15 degree. The truck's mass is 1.3 times 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 20% and (c) its speed is decreased by 23%?

Explanation / Answer

the speed is u = 172 km/h = 172 x (1000/3600) m/s = 172 x (5/18) m/s

the inclination is theta = 15o

the truck's mass is M = 1.3 x 10^4 kg

let the final speed of the truck is v = 0

we know that

v^2 - u^2 = 2aL

or L = (v^2 - u^2/2a)

where a = g x sin(theta),g = 9.8 m/s^2

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