Apilot flies her route in two straight-line segments. the displacement vector a for the first segment has a magnitude of 260 km and a direction 30.0o north of east. the displacement vector b for the second segment has a magnitude of 176 km and a direction due west. the resultant displacement vector is r = a + b and makes an angle θ with the direction due east. using the component method, find (a) the magnitude of r and (b) the directional angle θ.

First segment displacement is given as

so this is given in component form as

similarly the other displacement is given as

d2 = 176 km due west

now the total displacement is given as

part a)

magnitude of the displacement is given as

part b)

for the direction of displacement we can say

so it is 20.73 degree North of East

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."