Vector Calculus World Problem About Mechanics

[number0]

Homework Statement

A particle is constrained to move around the unit circle in the xy plane according to the

formula (x,y,z)=(cos(t²),sin(t²),0), t$$\geq$$0.

At what point on the circle should the particle be released to hit a target at (2,0,0)?

Homework Equations

None

The Attempt at a Solution

I computed the velocity vector and speed of the particle as functions of t:

velocity: (-2tsin(t²),2tcos(t²),0)

speed: 2t.

After wards, I got stuck. Any advice would be appreciated.

 

[gabbagabbahey]

Hint: Once the particle is released (No forces act on it), what kind of trajectory would you expect it to have? (i.e. circular, parabolic, etc.)