How can I calculate the max velocity for a car climbing a 15-degree hill?

[zacazac33]

velocity problem! NEED HALP ASAP!

hellloooo physics friends ok here's the issue:

A 3000-lb. car has an engine which can deliver 80-hp. to the rear wheels. What is the max velocity at which the car can climb a 15-degree hill?

We were told this must be answered tomorrow for part of our final, and I absolutely have no idea what to do. Help would be greatly appreciated!

-zac

 

[Hootenanny]

Are you sure it is velocity and not acceleration?

 

[chroot]

The velocity up the hill specifies a certain change in evelation per unit time.

Change in gravitational potential energy can be defined in terms of change in evelation. Since you know how fast the elevation is changing, you know how fast the gravitational potential energy is changing.

Energy per unit time is power.

To keep the car moving at a steady velocity up the hill, the engine is converting energy in the fuel into increasing gravitational potential energy at a rate of 80 hp, or about 60 kJ/s: http://www.google.com/search?hl=en&q=80+hp+in+joules/second&btnG=Google+Search

All you have to do is figure out what rate of elevation gain would require 60kJ/s to maintain.

- Warren