How Long Should a Ramp Be to Stop a Ford Ranger with Brake Failure?

[Tiffaney Sporl]

A Ford Ranger with a mass of 2430 kg is traveling at a velocity of 85 mph down a mountain road. The brakes fail and the driver elects to use a "run away" truck ramp to stop the vehicle. The ramp has an incline of 15.0 degrees. What is the minimum length the ramp must be in order for this strategy to stop the truck? Neglect friction and air resistance.

I found the KE at 1.75 x 10^6 J then set it equal to PE (mgh). This gave me a height of 73.559m. I used SOH to get a length of 284m. Is this correct?

 

[CWatters]

Forum rules require you to show your own attempt to solve the problem before help given.

 

[Tiffaney Sporl]

Forum rules require you to show your own attempt to solve the problem before help given.

Sorry I just added my attempt

 

[haruspex]

I found the KE at 1.75 x 10^6 J then set it equal to PE (mgh). This gave me a height of 73.559m. I used SOH to get a length of 284m. Is this correct?

Yes. You can make the working a bit simpler by noticing that the mass is irrelevant.