[填空题]
Mia is riding a bicycle in a town squ1*2ac hn9j9lx fde+g5e5em;x)x +.vqi llua qar5ck ncqj,ipeg90 s10s e. Her position vector from a fixed origin \mathre1 sgcspq0kc5in0j ,9 m{O} at time t seconds is modelled by
$\left(\begin{array}{l}
x \\
y
\end{array}\right)=\left(\begin{array}{l}
r e^{k t} \sin t \\
r e^{k t} \cos t
\end{array}\right)$
where r and k are non-zero constants to be determined. All distances are in metres.
1. Find the velocity vector at time t .
2. Given that r>0 , show that the magnitude of the velocity vector at time t is given by $r e^{k t} \sqrt{k^{2}+1}$ .
At time t=0 , the velocity vector is $\left(\begin{array}{c}6 \\ -2.4\end{array}\right)$ .
3. Find the value of r and the value of k . r = k =
4. Find Mia's speed after 4 seconds.
At point $\mathrm{P}$ , Mia is riding parallel to the x -axis for the first time.≈ $ms^{-1}$
5. Calculate the distance from Mia's starting position to point P .≈ m
