Solve for the Maximum Incline | Car Acceleration & Power Problem

[HT3]

Homework Statement

A 1100kg car can accelerate from 0-60kph in 6.5 seconds. With constant engine power, what is the steepest hill the car could climb at 20 kph.

Homework Equations

F=ma
W=Fd
P=W/t
g=mgSin(theta)

maybe work energy theorem?

The Attempt at a Solution

Not Much...just conversions and I do not know where to go from here
60kph-->16.67m/s
a=16.67/6.5 = 2.56m/s^2

20km/h --> 5.56m/s

 

[HT3]

bump please help :(

 

[Tlocc]

Okay so you need to think about the force of the car based on the mass and the acceleration. Draw yourself a diagram of an incline of steepness "S". Now put the car on it. You should have the force of the car moving up the incline and mg. You need to find the component of mg that matches the incline. Doing this, you can find a component that outweighs the force of the car moving forward. Hope that helps.

 

[HT3]

ok so would it be mgsintheta? but i don't have theta? so how can i get the netforce acting on the car

 

[Tlocc]

First find the force the car is exerting. What you want to do is insert that same force into your component of mg. You know the y component of mg by multiplication. So on the diagonal axis you will have a force equal and opposite to the car moving up the same axis, and then you will have mg on your y axis. Now you can use inverse trig to find the angle. Give that a try, I will be on for 20 more minutes before my next class.