Projectile motion with air resistance and earth

[zorro]

Homework Statement

A projectile near the Earth's surface (in 2 dimensions) is subjected to a resistive force F=-bv. The corrected value for time of flight is? (take r=b/m and initial velocity along y direction as Vo)

The Attempt at a Solution

Let instantaneous velocity vector V = Vxi + Vyj
Let the origin be fixed at the initial position.

dV/dt = -rV

What do I do next?

 

[ehild]

You can not ignore gravity.

ehild

 

[zorro]

Forgot about that
dV/dt = -rV - gj

 

[ehild]

In general, you should write and solve the differential equations both for the x and y component of the velocity.

ehild

 

[zorro]

Is there any other method to find out the time of flight directly?
Will the time taken be greater or less than the normal t=2usin(theta)/g ?

 

[ehild]

Look at the initial velocity given in the problem. Is it a two-dimensional motion really?
What do you mean on other method to find out time of flight directly? You want a formula to plug in data? I think you are supposed to derive it and I thought you were able to do it. But anyway, you find the formula here. http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

ehild

 

[zorro]

Look at the initial velocity given in the problem. Is it a two-dimensional motion really?

That is the initial velocity along y-direction (component of velocity)

After solving the D.E., I got
gT/r = (rVoy + g)(1-e^-rT).

The answer given is T=2Voy/(g-rVy) [Is this wrong?]