Solving Mechanics Problems: Truck Movement on Hills & Ramps

[anathema]

These are two separate questions, each of them together, in a way.

1. A truck rolls down a 7.8 degree hill with a constant speed of 30.0 m/s. At the bottom of the hill it continues on a horizontal surface. How far will the truck go before it stops?

For this I made a diagram with a right-angle triangle where the hypotenuse of the triangle was gravity, and the shortest side was the hill the truck was moving on. I discovered its deceleration due to friction by multiplying gravity by the sin of 7.8, mass being irrelevant. From this I used the formula vf^2 = vi^2 + 2 * ad,
giving me 0 = 30^2 + 2*-1.33136*d. The d I got was 338 m.

2. The truck instead goes up a 15-degree ramp with a kinetic coefficient of friction of 0.8. How far would it go? What is its deceleration?

I made the slope hill the X axis in a diagram, and determined that two forces were responsible for deceleration, friction and the x component of gravity, each pointing opposite to the movement of the truck. 9.81*sin(15) + 9.81*0.8 = deceleration, which, when used with the same formula as above gave me 43.3 as the distance.

I have an awkward feeling that I didn't do these problems right, and I know my explanations sound confusing when the diagrams aren't there. Any help?

 

[arcnets]

Hi anathema,
1. looks OK IMO.
2. looks wrong. I think you should take into account that only the normal component of gravity contributes to friction.

 

[anathema]

Thanks! Yeah that's what I discovered too, that I had to take the normal component of gravity to use for friction. In either case I changed them in time and both questions were marked correctly.