DE Derivative Using Euler's Method

[MechE2015]

Homework Statement

The velocity v of a skydiver is well modeled by a differential equation:

m*dv/dt = mg - k*v^2

Where m is the mass of the skydiver, g = 9.8 m/s^2 is the gravitational constant, a k is the drag coefficient determined by the position of the diver during the dive. Consider a diver of mass m = 54 kg with a drag coefficient of 0.18 kg/m. Use Euler's method to determine how long it will take the diver to reach 95% of her terminal velocity after she jumps from the plane.

Homework Equations

Euler's method:
y[k+1] = y[k] + f(t[k],y[k])*DeltaT

The Attempt at a Solution

I placed the constants into the equation to get:
dv/dt = (529.2 - 0.18*v^2) / 54

Then, using Euler's method with a very small delta T, I find terminal velocity to be 54.2218. This would mean that the diver reaches 95% of terminal velocity at approximately 51.5107.

1) Is this the correct way of approaching the problem? Is my terminal velocity correct?
2) From here I suppose I would just find the point where y[n] = 51.5107?

If anyone can help me I would greatly appreciate it!

 

[Dick]

Homework Statement

The velocity v of a skydiver is well modeled by a differential equation:

m*dv/dt = mg - k*v^2

Where m is the mass of the skydiver, g = 9.8 m/s^2 is the gravitational constant, a k is the drag coefficient determined by the position of the diver during the dive. Consider a diver of mass m = 54 kg with a drag coefficient of 0.18 kg/m. Use Euler's method to determine how long it will take the diver to reach 95% of her terminal velocity after she jumps from the plane.

Homework Equations

Euler's method:
y[k+1] = y[k] + f(t[k],y[k])*DeltaT

The Attempt at a Solution

I placed the constants into the equation to get:
dv/dt = (529.2 - 0.18*v^2) / 54

Then, using Euler's method with a very small delta T, I find terminal velocity to be 54.2218. This would mean that the diver reaches 95% of terminal velocity at approximately 51.5107.

1) Is this the correct way of approaching the problem? Is my terminal velocity correct?
2) From here I suppose I would just find the point where y[n] = 51.5107?

If anyone can help me I would greatly appreciate it!

Sure, terminal velocity is where dv/dt=0. You don't even need the numerical solution to find the terminal velocity. So that part looks ok, and yes, find where y[n] = 51.51.