# Projectile problem

• Feb 10th 2009, 01:06 PM
jackiemoon
Projectile problem
Hey,

Can anybody offer any assistance with the following problem please?

A projectile is shot, in windy conditions, with initial speed v at an angle of 60 degrees from the ground. Because of the wind, which blows horizontally, the projectile is subject to a viscosity force, in the direction of the wind, of the form Fv = -c.vx (where vx is the component of the velocity of the projectile in the horizontal direction and c is a constant).

[nb. In Fv = -c.vx, the first v and x are subscript. Hope the question is clear. I don't how to type subscript characters.]

Determine the position of the projectile, x(t) and y(t), for t ≥ 0 and compute the distance at which the projectile lands.

I'd be very grateful for any help with this.

Thanks
• Feb 10th 2009, 04:08 PM
skeeter
Quote:

Originally Posted by jackiemoon
Hey,

Can anybody offer any assistance with the following problem please?

A projectile is shot, in windy conditions, with initial speed v at an angle of 60 degrees from the ground. Because of the wind, which blows horizontally, the projectile is subject to a viscosity force, in the direction of the wind, of the form Fv = -c.vx (where vx is the component of the velocity of the projectile in the horizontal direction and c is a constant).

[nb. In Fv = -c.vx, the first v and x are subscript. Hope the question is clear. I don't how to type subscript characters.]

Determine the position of the projectile, x(t) and y(t), for t ≥ 0 and compute the distance at which the projectile lands.

I'd be very grateful for any help with this.

Thanks

$F = -cv_x$

$m\frac{dv_x}{dt} = -cv_x$

$\frac{dv_x}{dt} = -\frac{c}{m}v_x$

let $\frac{c}{m} = k$ ...

$\frac{dv_x}{dt} = -kv_x$

$v_x = v_{xo}e^{-kt}
$

you also know that $v_{xo} = v_o\cos(60) = \frac{v_o}{2}$