Projectile motion with air resistance

**Jeonsah** · February 27th 2011, 07:47 PM

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?

**topsquark** · February 27th 2011, 08:04 PM

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

**Jeonsah** · February 27th 2011, 08:04 PM

Thank you!

Thread: Projectile motion with air resistance

LinkBack

Thread Tools

Display

Projectile motion with air resistance

Similar Math Help Forum Discussions

Projectile Motion

Motion with resistance problem

Motion equation of a free falling object, with air resistance

[Help Me!] Linear motion equations with drag resistance

Projectile Motion with vector functions (3D Motion in space velocity)

Search Tags