1. ## 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

2. 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 $v_{xo} = v_o\cos(60) = \frac{v_o}{2}$