How Do You Calculate the Radius of Curvature for a Projectile's Trajectory?

[Chantry09]

Homework Statement

A projectile is fired at an angle of 30 degrees above the horinzontal with a velocity V0 of 460 m/s. Determine the radius of the curvature of the trajectory at the position of the particle 10 seconds after firing.

Homework Equations

V = U + AT

The Attempt at a Solution

By working out the speeds of the x and y components 10 seconds into the flight I've worked out the projectile is facing 39.466 degrees below the horizontal. However, now that i know the angle of the projectile 10 seconds into its journey, how do i work out the "radius of the curvature"?

Any help would be much appreciated.

James

 

[HallsofIvy]

You should have been able to calculate the precise formula for y as a function of x. (It should be a parabola.) Do you know how to calculate "curvature" from that? Radius of curvature is just the reciprocal of curvature.

 

[Chantry09]

I don't know how to calculate that, no. The teacher just said i had to work out the forces acting in the x and y direction at t=10 so that's what i did. If you could explain the next step or what i should have done that would be great.