A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30.0 $\degree$ north of east.What is the new velocity and direction of the aircraft?
A)607 mph,5.67 $\degree$N of E
B)620 mph,5.67 $\degree$ N of E
C)607 mph,6.22 $\degree$N of E
D)588 mph,4.87 $\degree$ N of E

Question

Quizplus · Accepted Answer

To find the new velocity and direction of the aircraft, we need to add the vector of the wind to the vector of the aircraft's velocity. We can break down the vectors into their components:
Aircraft velocity: 500 mph due east = 500i 
Wind velocity: 120 mph at 30° north of east = 120(cos 30° i + sin 30° j)

To add the vectors, we simply add the i and j components separately:
New velocity = (500i) + (120cos 30° i + 120sin 30° j) 
= (500 + 120cos 30°)i + (120sin 30°)j 
= (570.6i + 60j) mph

To find the direction of the new velocity, we need to find the angle it makes with due east. We can use the arctan function to find the angle:
tanθ = (60)/(570.6) 
θ = 5.67° north of east

Therefore, the new velocity and direction of the aircraft is 607 mph, 5.67° north of east. Option A is the correct answer.

A Jet Airliner Moving at 500 Mph Due East Moves °\degree°

A Jet Airliner Moving at 500 Mph Due East Moves $\degree$