Help with mechanical energy question? what was initial speed?

A semitrailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway-truck ramp that is inclined at an angle of 16.0° above the horizontal. The semitrailer coasts to a stop after traveling 143 m along the ramp. What was the truck's initial speed? Neglect air resistance and friction.

we know that vf^2=v0^2+2ad where vf=final speed =0 v0=initial speed (to be determined) a=acceleration d=distance = 143m so if we can find the acceleration, we can find the initial speed we are told that the truck coasts up an incline of 16 degrees; neglecting friction (a really bad assumption, btw), we have that the force acting on the truck is the component of gravity acting down the plane, so newton's second law is: F = ma mg sin (theta) = ma or a=gsin(theta) here, a = g sin 16 = 9.8sin16=2.7m/s/s so we have vf^2=v0^2+2ad 0=v0^2+2(-2.7)(143) (minus sign for a means accel opposes motion) v0^2=772.2 v0=27.8m/s/s

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