Answer
(a) The jetliner is 872.8 km from the starting point.
(b) The jetliner could have flown directly to the destination at an angle of $9.9^{\circ}$ south of east.
(c) The flight took 2.25 hours.
(d) A direct flight would have taken 2.18 hours.
Work Step by Step
(a) We can find the total distance the jetliner flies east:
$600.0~km+(300.0~km)~cos~30.0^{\circ} = 859.8~km$
We can find the total distance the jetliner flies south:
$(300.0~km)~sin~30.0^{\circ} = 150.0~km$
We can find the distance from the starting point:
$\sqrt{(859.8~km)^2+(150.0~km)^2} = 872.8~km$
The jetliner is 872.8 km from the starting point.
(b) We can find the angle $\theta$ south of east:
$tan~\theta = \frac{150.0~km}{859.8~km}$
$\theta = tan^{-1}(\frac{150.0~km}{859.8~km})$
$\theta = 9.9^{\circ}$
The jetliner could have flown directly to the destination at an angle of $9.9^{\circ}$ south of east.
(c) We can find the time of the flight:
$t = \frac{600.0~km+300.0~km}{400.0~km/h} = 2.25~h$
The flight took 2.25 hours.
(d) We can find the time of a direct flight:
$t = \frac{872.8~km}{400.0~km/h} = 2.18~h$
A direct flight would have taken 2.18 hours.
