Multivariable Calculus unit derivatives question

[kelang]

Homework Statement

The position on the ground in the xy plane that is hit by the sun given by (x,y)=(3t+tan(phi), -2t+tan(theta)), where t, phi, and theta, are controlled input variables. What is the velocity of the hit point if the input variables are at values (5, pi/4, pi/3) and changing with velocity (1, 3, -2)? What is the speed of the hit point?

Homework Equations

The Attempt at a Solution

I know the parametric curve would be (5-t, (pi/4)+3t, (pi/3)-2t), but I'm confused as to how to make the components of this using linear algebra. Also, how would I find speed at the point? Would that be ds/dt, which is (ds/dx)/(dx/dt)? If so how would I do that? If someone could offer hints if they didn't have time to completely solve it that would be great as well!


Thanks so much!

 

[Ray Vickson]

By calculation you know x(5) and y(5) because you know phi(5) and theta(5). If t = 5 + h, with h > 0 small, what are the new phi(5+h), theta(5+h), x(5+h) and y(5+h)? What do the latter become if you keep only terms up to first order in h?

RGV