How to Calculate Bearing in Physics

Understanding How to Calculate Bearing in Physics

In this post, I will guide you on how to calculate bearing in physics. But we need to first understand the definition of bearing.

Definition: Bearing is the angular dispalcement or direction between cardinal points in an x – y plane.

To find the direction of an object, we need to have a look at a plane or space. By looking at the four cardinal points from the perspective of a plane, it is obvious that we have x and y cordinates and we call them abcissa and ordinate respectively.

Additionally, we assign names to these four cardinal points or poles, and we call them north, south, west, and east.

While calculating bearing,we use the symbol of θ to indicate the angular direction of an object. Here are some the methods we apply to measure angular direction (θ):

• Applying compass
• Using protractor on a map
• Simple calculation

In this article, I will solve few examples that will guide you on how to calculate bearing in physics.

Examples of How to Calculate Bearing in Physics

We have four cardinal points starting from North (N) to East (E), from N to E covers an angle of 90⁰. Depending on the direction of the object, the angle between two cardinal points is 90⁰.

This makes movement from North to East, and then to South 180⁰

From North to East to South and then to West 270⁰.

And complete movement from North, East, South, West, and back to North 360⁰

After finding the direction of the object, this is how you write it:

Assuming your θ is 60⁰, you now know that the direction θ=60⁰ is between North and East

Thus, you write it as N 60⁰E

Which means sixty degrees from North direction towards East

Now, here are few examples to guide you understand how to calculate bearing in physics

Example 1

A man walks 4 kilometer due Northand then walks 3km due East. What is his displacement from the starting point.

Solution

Data

We first extract our data from the above question

Let us assume that his initial position is the origin O

He walks from his origin O to another point A due North = 4 kilometer

Additionally, He walks from his second position A to another location B due East = 3 kilometer

For us to find his displacement from the starting point, we calculate OB.

To calculate OB, we apply the formula below

OB² = OA² + AB²

We have OB = ?, OA = 4km, and AB = 3km

Substituting the above values into the formula, we have

OB² = 4² + 3² = 16 + 9 = 25

Therefore we take the square root of both sides, to find OB

OB = √25 = 5km

Now we can see that the dispalcement of the man from his initial position is 5km.

We need to also find the direction, θ

By applying the formula below, we have

tan θ = AB/OA = 3/4

Devide both sides by tan to find θ

θ = tan^-1 (3/4) = tan^-1 (0.75) = 36.9⁰

We can now approximate θ as 37⁰ which is the direction of the man

θ = 37⁰

Because 37⁰ is between North(N) and East (E), we can now say that the direction of the man is N 37⁰E ( The man is thirty seven degrees from North direction towards East)

Therefore, our final answer is as follows:

The displacement is 5km, N 37⁰E

Example 2

Find the location of A(3,-6) and B(7,9) with the reference to a point (0,0) and determine the bearing of A,

Solution:

Data:

Let us consider triangle OAB

When we trace our line on B axis from Origin(which is zero) to be on A(3,-6), we can see that X₁ = 3 and this implies that OB = X₁ = 3

Therefore, modulus of OB= 3 units

modulus of AB= 6 units

We now apply the formula below

tan θ = OB/AB = 3/6

By making θ subject of the formula, we have

θ = tan^-1 (0.5) = 26.6⁰

Which can be approximated into

θ = 27⁰

To find the bearing of A, we add 27⁰ to the 90⁰ which si being completed from North to East

Therefore, A = 90⁰ + 27⁰ = 117⁰

Which is considered as E 117⁰S

Example 3

A butterfly moves from a point X to a point Y, a distance of 15 meters in the direction 045⁰. It then changes direction and moves to a point Z, in the direction 155⁰. If the point Z is due east of X, find the distance of the point Z from the point Y.

Solution

Data

By applying the sine rule which is

X / Sinθ₁ = Y / Sinθ₂ = Z / Sinθ₃

and θ₁ = 45⁰, θ₂ = 70⁰, θ₃ = 65⁰, Z = 15m, and X = ?

we now substitute the above data into X / Sinθ₁ = Z / Sinθ₃

X / Sin45⁰ = 15 / Sin65⁰

We can now cross multiply the above equation

XSin65⁰ = 15 x Sin45⁰

We now make X subject of the formula

X = (15 x Sin45⁰) / (Sin65⁰) = (15 x 0.71) / (0.91) = 10.65/0.91 = 11.7m

Therefore the distance of the point Z from the point Y which is X = 11.7 meters

You may like to read:

How to calculate velocity ratio of an inclined plane

Reference:

Wikipedia