Projectile motion with air resistance and earth

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Homework Help Overview

The problem involves analyzing the motion of a projectile near the Earth's surface while considering air resistance, modeled by a resistive force proportional to velocity. The original poster seeks to determine the corrected time of flight, given specific initial conditions and parameters.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to set up the problem using differential equations for velocity, while some participants emphasize the importance of including gravitational effects. Questions arise regarding alternative methods to calculate time of flight and the validity of the derived formula.

Discussion Status

Participants are exploring various aspects of the problem, including the necessity of incorporating gravity and the dimensionality of the motion. There is an ongoing dialogue about the correct approach to derive the time of flight, with some guidance provided on solving differential equations.

Contextual Notes

There are indications of confusion regarding the initial conditions and the nature of the motion, as well as a reference to external resources for further clarification.

zorro
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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?
 
Last edited:
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You can not ignore gravity.

ehild
 
Forgot about that
dV/dt = -rV - gj
 
In general, you should write and solve the differential equations both for the x and y component of the velocity.

ehild
 
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 ?
 
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
 
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?]
 
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