Solve Vehicle Physics Problem: Find Maximum Ground Speed with Headwind

[hallo]

Hi,

A vehicle land on a mountain of 4400ft.The Engine delivers 400hp to the wheels and careful streamlining has resulted in a drag coefficient of 0.5,based on a 20ft^2 frontal area.Compute the maximum ground speed of the car in i)still air and ii)with a 20mph head wind

for part i)I have solve using coefficient power and drag coefficient formulas.However the part ii), I am haveing problem.

Pls help.
thanx

 

[Astronuc]

If one solve part i, then part ii should be solvable.

With a head wind, the maximum vehicle velocity is reduced.

How does one solve for V_max?

If one sets up an equation in V, then with a headwind try V+V_head, where V_head is the headwind velocity.

 

[hallo]

I have solve till Velocity but not V(max). my eqn is
Power= drag coeff * 1/2 * Area * density* velocity^3

to find V(max),what should I set to zero and then differentiate?? ??