$(1)$ The ground radar is tracking the motion of an airplane that is flying in a straight line, gaining altitude at a climb angle of $=25$ shown. At a certain instant the recorded data indicate $r=1500ft,=35$ measured from the vertical, $r^{}=360f\frac{t}{sec},$ and ${}^{}=-0\mathrm{.}07ra\frac{d}{se{c}^2}.$ Determine the plane's velocity $v,$ acceleration $a,$ and the values of ${}^{}$ and $r^{}$ for this position.

Ans: $v=416f\frac{t}{s},a=10\mathrm{.}47f\frac{t}{se{c}^2}$ slowing down, ${}^{}=0\mathrm{.}1386ra\frac{d}{sec,r^{}}=19\mathrm{.}73f\frac{t}{se{c}^2}$

If possible can you try solving this with vector math and anntate the drawing, thank you!