Dynamics S2 slide 4: Radar-tracked aeroplane (ENGR5004)

Dynamics S2 slide 4: Radar-tracked aeroplaneFrom lectureCurrent specThird3 marks3 min

ENGR5004 Dynamics Session 2, slide 4 (Applications of a particle in curvilinear motion)

The path of motion of a plane can be tracked with radar and its $x$ , $y$ and $z$ coordinates (relative to a point on earth) recorded as a function of time.

How can we determine the velocity or acceleration of the plane at any instant?

Formulas you may need

$\mathbf r = x\mathbf i + y\mathbf j + z\mathbf k$ , $\mathbf v = \dot x\mathbf i + \dot y\mathbf j + \dot z\mathbf k$ , $\mathbf a = \ddot x\mathbf i + \ddot y\mathbf j + \ddot z\mathbf k$ (learn this)
$v = \sqrt{v_x^2 + v_y^2 + v_z^2}$ , $a = \sqrt{a_x^2 + a_y^2 + a_z^2}$ (learn this)