Respuesta :
Answer: 180° + angle.
Step-by-step explanation: The plane must fly at
12
0
∘
120
∘
to return directly back to City A
1Calculate the total distance traveled in the first leg of the journey.
Given the speed of 280 mph and time of 2 hours, use the formula: distance = speed * time.
Distance = 280 mph * 2 hours = 560 miles.
2Calculate the total distance traveled in the second leg of the journey.
Given the speed of 240 mph and time of 1.5 hours, use the formula: distance = speed * time.
Distance = 240 mph * 1.5 hours = 360 miles.
3Draw a vector diagram to represent the two legs of the journey.
Let the first leg be represented by a vector of 560 miles at
21
0
∘
210
∘
and the second leg by a vector of 360 miles at
32
0
∘
320
∘
.
4Find the resultant vector of the journey.
To find the resultant vector, add the two vectors using vector addition. This can be done by breaking the vectors into x and y components and then adding them up.
5Calculate the x-component of the resultant vector.
x-component = 560 miles * cos(
21
0
∘
210
∘
) + 360 miles * cos(
32
0
∘
320
∘
).
6Calculate the y-component of the resultant vector.
y-component = 560 miles * sin(
21
0
∘
210
∘
) + 360 miles * sin(
32
0
∘
320
∘
).
7Find the direction of the resultant vector.
Use the arctan function to find the angle of the resultant vector: angle = arctan(y-component / x-component).
8Convert the angle to the appropriate direction.
The direction of the plane to return directly back to City A is the direction opposite to the angle calculated in Step 7.
9Calculate the final direction.
Final direction = 180° + angle.
