Kinematics of a Particle: Curvilinear Motion

A radar is tracking a rocket. At some instant of time, the distance, r measured as 10 mi and angle 30º. Determine the velocity and
acceleration of the rocket.

Velocity: v = ds/dt, Acceleration: a=dv/dt
Relationship Displacement- velocity –acceleration: ads = vdv
Absolute Circular Motion- Angular Velocity: ω =dθ/dt
Angular Acceleration: α= dω/dt= d^2θ/dt^2
Relationship Displacement - Velocity – Acceleration: ωdω = αdθ

Ok I know that the derivatives of r are: 650 ft/s , 165 ft/s^2 , and the derivates of the angle 30º are estimated to be: 0.031 rad/s, and 0.005 rad/s^2. That is all the info I have. I converted the 10 mi= 52,800 ft. And the professor gave us the answers: the velocity is supposed to be: 1761 ft/s and the acceleration 325 ft/s^2 I just don't know how to get there.
Last edited:
Never mind. I was looking at the wrong formulas. This is the one:
velocity= square rootof of[650^2+(52,800)(0.031)^2]=1761 ft/s

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