Vectors Applications: Solving Pilot Trip from City A to City B

In summary, the pilot should take a heading of 073 degrees and the trip will take approximately 1.10 hours.
  • #1
kaybaby
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Homework Statement



A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 70 degrees. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110 degrees. What heading should the pilot take to reach his or her destination? How long will the trip take?

Homework Equations


Cartesian Vectors Equations


The Attempt at a Solution


I am not sure whether i did right

First, alpha=90-70 degress=20 degrees
Let a be the direction of the 2 cities.
a=[x,y]
cos theta=cos 20=x/720
sin theta=sin 20= y/720
a=[720cos20, 720 sin 20]
a=[676.58,246.25]

Let w be the direction of wind.
110-90=20 degrees
w=[x,y]
cos y=cos20=x/60
siny = sin20=y/60
w=[56.38, =20.52]

let p be the vector of the plane
p=a+w
p=[732.96,225.73]

|p|=sqre root of 732.96^2+225/73^2
|p|= 766.93 km

time = distance/speed
=766.93km/700 km/h
=1.10 h

Since p=[732.96,224.73] we can use this info to find out the directional angle, B.
tan B=225.73/732.96
=17.12 degrees.
90-17.12 =72.88 degrees

The pilot should take the heading of 072.88 degree to reach his/her destination. It takes approx 1.10 hours.
 
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  • #2


Your solution looks correct, but I would suggest using the Pythagorean theorem to find the magnitude of p instead of calculating the square root of the components separately. Also, I would recommend rounding your answer for the heading to the nearest degree. Additionally, it might be helpful to draw a diagram to visualize the problem and your solution. Overall, good job on solving the problem!
 

FAQ: Vectors Applications: Solving Pilot Trip from City A to City B

1. What are vectors and how are they used in solving a pilot trip from City A to City B?

Vectors are mathematical quantities that have both magnitude and direction. They are used in solving a pilot trip from City A to City B by representing the displacement of the plane from its starting point (City A) to its destination (City B) as a vector. This allows for the calculation of the distance, speed, and heading of the plane, as well as any necessary adjustments for wind or other factors.

2. How do you determine the magnitude and direction of the vector representing the displacement of the plane?

The magnitude of the vector can be calculated using the Pythagorean theorem, where the length of the vector is equal to the square root of the sum of the squares of its components (representing the distance traveled in the x and y directions). The direction can be determined using trigonometric functions, such as tangent or sine, depending on the given information.

3. How can vectors be used to adjust for wind or other factors during a pilot trip?

Vectors can be used to represent the force and direction of wind or other factors affecting the plane's movement. By adding this vector to the original displacement vector of the plane, the adjusted displacement and direction can be calculated. This allows the pilot to make necessary adjustments to stay on course.

4. Can vectors also be used to calculate the time of the pilot trip?

Yes, vectors can also be used to calculate the time of the pilot trip. By dividing the distance of the displacement vector by the speed of the plane, the time can be determined. This calculation can be adjusted to account for any changes in speed due to wind or other factors.

5. Are there any limitations to using vectors for solving a pilot trip from City A to City B?

While vectors are a useful tool for calculating the displacement, distance, speed, and direction of a pilot trip, they may not account for all factors affecting the trip, such as air traffic or unexpected weather conditions. Additionally, the accuracy of the calculations may be affected by the precision of the given information and any assumptions made in the calculations.

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