Calculating Deceleration of Man on Bicycle with Air Resistance

[furor celtica]

Homework Statement

A man on a bicycle, of total mass 100 kg, is free-wheeling at a constant speed of 15ms^-1 down a hill with a gradient 10% (i.e. sin^-1(0.10)). He wants to slow down to a safer speed, so he applies the brake lightly to produce a constant braking force of 84 N. The air resistance is proportional to the square of the speed.
a. Calculate the deceleration when he first applies the brake.

Homework Equations

The Attempt at a Solution

Several other questions follow.
Anyway the problem is the air resistance: in this model I know v^2 but I don’t know the constant k as in kv^2! I know how to solve these problems with k but without it I’m lost. Is there a way to work around the air resistance, i.e. without using k?

 

[Stonebridge]

As he is freewheeling at constant speed initially, we know that there is no resultant force on him. (No acceleration) This means that the air resistance must be exactly balanced by the component of the weight (man + cycle) down the slope.