Question

Kinematics Question Please Help.

Answer 1

The velocity of the air relative to the ground is

$\vec v_{A/G}=\left(95\,\frac{\rm km}{\rm h}\right)(\cos30.0^\circ\,\vec\imath+\sin30.0^\circ\,\vec\jmath)$

The velocity of the plane relative to the air is

$\vec v_{P/A}=\left(301\,\frac{\rm km}{\rm h}\right)(\cos\theta\,\vec\imath+\sin\theta\,\vec\jmath)$

where $\theta$ is the direction the plane needs to point so that the resultant vector - the velocity of the plane relative to the ground - is

$\vec v_{P/G}=\vec v_{P/A}+\vec v_{A/G}=v(\cos13.0^\circ\,\vec\imath+\sin13.0^\circ\,\vec\jmath)$

Here $v$ is the speed of the plane relative to the ground.

So we have

$\begin{cases}v\cos13.0^\circ=\left(95\,\frac{\rm km}{\rm h}\right)\cos30.0^\circ+\left(301\,\frac{\rm km}{\rm h}\right)\cos\theta\\v\sin13.0^\circ=\left(95\,\frac{\rm km}{\rm h}\right)\sin30.0^\circ+\left(301\,\frac{\rm km}{\rm h}\right)\sin\theta\end{cases}$

Use a calculator to solve for $v$ and $\theta$; you should find

$v=390\,\frac{\rm km}{\rm h}$

$\theta=7.7^\circ$