Projectile Trajectory Radius Calculation: 30° Angle, 460m/s Velocity, 10s Time

[Chantry09]

Homework Statement

A projectile is fired at an angle of 30 degrees above the horizontal 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
s = ut + 0.5at(squared)
v(squared) = u (squared) + 2 as

The Attempt at a Solution

No idea. I am trying to do this question but i haven't been taught how to work out the angles during flight. Can anyone help?

 

[Chantry09]

Bump, i still can't work this out.

 

[HallsofIvy]

First determine the trajectory! Of the equations you wrote
v = u + at
s = ut + 0.5at(squared)
v(squared) = u (squared) + 2 as
Only s= ut+ 0.5at² will help and you need to convert into x and y coordinates. Of course the acceleration vector a= <0, -9.8> so the equations for x and y separately are x= u_x t and y= u_y- 4.9t².

You have an speed 460 m/s and angle 30 degrees. Do you know how to find the x and y components of velocity? Once you do that you have equations for x and y depending on the parameter t.

"Determine the radius of the curvature of the trajectory at the position of the particle 10 seconds after firing."

If you are expected to be able to do this, then you must have been given formulas for "curvature" and "radius of curvature". Do you know a formula for the radius of curvature of a graph in the xy plane where x and y are given as functions of a parameter?

 

[Chantry09]

unfortunately i haven't been given any equations for the curvature. Either I am missing something, or do you think it could mean the radius of the curve is the height of the ball at that time, and take that height as the radius.

It doesn't really make sense considering its not a circle its a parabola. Thank you for your help, do you have any idea what he could mean in the question if I am not given an equation for the radius of the curvature?

 

[Chantry09]

Bump, really need help with this.