Maximum speed pulling a trailer up a 12-degree hill

[doug1]

Homework Statement

You are driving home from the cottage and pulling a trailer behind your car. There is a steep hill with a 12 degree incline that you must drive up. You read the instructions for the trailer hitch which keeps the trailer attached to your car. The hitch can withstand a maximum force of 4.3 x 10^3 N. The car has a mass of 1.1 x 10^3 kg. The trailer has a total mass (including the stuff inside) of 2.7 x 10^2 kg. There is rolling friction between the trailer and road with μr = 0.15 (treat this just like kinetic friction). You start from the bottom of the hill at rest (a stop sign). What is the top speed you could achieve after driving 45.0 m up the hill?

The Attempt at a Solution

I drew a FBD of the trailer and then made the assumption that the maximum Ft (force of tension) pulling the trailer is 4.3 x 10^3 N. I then isolated variable 'a', and ascertained an acceleration of 14.5 m/s^2.

I then determined the maximum velocity to be 36 m/s. Can anyone verify this value?

 

[shake94]

Your procedure seems right. Hopefully you included all other forces such as the Normal and the Friction into your calculation.

 

[haruspex]

ascertained an acceleration of 14.5 m/s^2.

I only get 12.45. Did you perhaps omit the component of gravity parallel to the slope?