# A confusing word problem. Can any one solve it?

## Homework Statement

A 240gram toy car is driven by an electric motor that has a constant power output. The car can climb a 24° incline at 16m/s and can travel on a horizontal table at 39m/s. The frictional force retarding the motion is kv, where k is a constant and v is its speed. How steep an incline can it climb with a speed of 28m/s?

## The Attempt at a Solution

I've tried solving this for 2 days now and but not succeeded. It seems quite simple but it is the kv part that I don't know how to use.
Please could someone explain how to solve it?

Help is very much appreciated!
Thank you!

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berkeman
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## Homework Statement

A 240gram toy car is driven by an electric motor that has a constant power output. The car can climb a 24° incline at 16m/s and can travel on a horizontal table at 39m/s. The frictional force retarding the motion is kv, where k is a constant and v is its speed. How steep an incline can it climb with a speed of 28m/s?

## The Attempt at a Solution

I've tried solving this for 2 days now and but not succeeded. It seems quite simple but it is the kv part that I don't know how to use.
Please could someone explain how to solve it?

Help is very much appreciated!
Thank you!
Welcome to the PF.

The k*v part is just like wind resistance and/or rolling resistance. They are saying that the only retarding force on flat ground is this resistance, which is proportional to velocity.

Do the 3 FBDs for the 3 cases, and include this resistant force in each. You should end up with a set of equations that you can use to solve for the velocity in the 3rd situation. Please show us your work...

Oh thank you :)
I still seem to be going in circles.

I made a table with the kinetic and potential energies for each one: (by the way the speeds are supposed to be in cm/s - i typed it wrong)

1) 0.39m/s --> Kinetic E = m(v^2)/2 = 0.018252 J
Potential E = mgh = 0 J

2) Kinetic = 0.003072 J
Potential = 0.1531 J

3) Kinetic = 0.009408 J
Potential = ?? (i don't know theta, that is what i need to find)

So i guess 2) is best to work with since i have both values so i can find friction:
so friction is PE - KE = 0.1531 - 0.003072 = 0.150028 J

I have no idea if this is right...
and how do i include the "motor has a constant power output" ?

0.39m/s

PhanthomJay