Answer
(a) The average speed is $112~km/h$
(b) The average velocity is $97.3~km/h$
Work Step by Step
(a) We can find the distance traveled directly east:
$(96~km/h)(1.0~h) = 96~km$
We can find the distance traveled east of north:
$(128~km/h)(1.0~h) = 128~km$
We can find the average speed for the trip:
$average~speed = \frac{distance}{time}$
$average~speed = \frac{224~km}{2.0~h}$
$average~speed = 112~km/h$
The average speed is $112~km/h$
(b) We can find the east component of the displacement:
$96~km+(128~km)~sin~30.0^{\circ} = 160~km$
We can find the north component of the displacement:
$(128~km)~cos~30.0^{\circ} = 110.9~km$
We can find the magnitude of the displacement:
$\sqrt{(160~km)^2+(110.9~km)^2} = 194.68~km$
We can find the average velocity $v_{av}$:
$v_{av} = \frac{displacement}{time}$
$v_{av} = \frac{194.68~km}{2.0~h}$
$v_{av} = 97.3~km/h$
The average velocity is $97.3~km/h$
