# Projectile motion with air resistance

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• Feb 27th 2011, 08:47 PM
Jeonsah
Projectile motion with air resistance
Hey guys, im having a little bit of trouble with a problem. Here it is:

$m\frac{dv}{dt} = mg - kv^2$

Consider the 16-pound cannonball sht vertically upward with an initial velocity of 300ft/s. Deterine the maximum height attained by the cannonball if air resistance is assumed to be proportional to the swaure of the instantaneous velocity. Assume that the positive direction is upward and take k = 0.0003.
[hint: Slightly modify the DE above]

Where do I start?
• Feb 27th 2011, 09:04 PM
topsquark
Quote:

Originally Posted by Jeonsah
Hey guys, im having a little bit of trouble with a problem. Here it is:

$m\frac{dv}{dt} = mg - kv^2$

Consider the 16-pound cannonball sht vertically upward with an initial velocity of 300ft/s. Deterine the maximum height attained by the cannonball if air resistance is assumed to be proportional to the swaure of the instantaneous velocity. Assume that the positive direction is upward and take k = 0.0003.
[hint: Slightly modify the DE above]

Where do I start?

The differential equation is separable:

$\displaystyle \frac{dv}{g - \frac{k}{m}v^2} = dt$

-Dan
• Feb 27th 2011, 09:04 PM
Jeonsah
Thank you!