Question

12. Jack and Jill heard a noise in the woods and both ran off in different directions. Jack's

GPS informs him that he ran 29 m at a bearing of 40 degrees South of East and Jill's
compass watch indicates that she ran 42 m at an angle of 11 degrees South of West.
What is the displacement from Jill to Jack at this point?

Answer 1

Answer: To find the displacement from Jill to Jack, we can use vector addition since they both ran off in different directions.

Let's break down their movements into components:

For Jack's movement:

Distance (magnitude) = 29 m

Direction (bearing) = 40 degrees South of East

For Jill's movement:

Distance (magnitude) = 42 m

Direction (bearing) = 11 degrees South of West

Now, let's convert the directions into Cartesian coordinates (x and y components):

For Jack:

x-component = 29 m * cos(40 degrees) [Since it is in the positive x-direction]

y-component = -29 m * sin(40 degrees) [Since it is in the negative y-direction]

For Jill:

x-component = -42 m * cos(11 degrees) [Since it is in the negative x-direction]

y-component = -42 m * sin(11 degrees) [Since it is in the negative y-direction]

Now, add the x-components and y-components separately to get the total displacement:

x-displacement = (29 m * cos(40 degrees)) + (-42 m * cos(11 degrees))

y-displacement = (-29 m * sin(40 degrees)) + (-42 m * sin(11 degrees))

Calculate these values using a calculator:

x-displacement ≈ 29 * 0.766 + (-42 * 0.981) ≈ 22.214 - 41.242 ≈ -19.028 m

y-displacement ≈ (-29 * 0.643) + (-42 * 0.190) ≈ -18.647 - 7.98 ≈ -26.627 m

Now, use the Pythagorean theorem to find the magnitude of the total displacement:

Displacement = √((-19.028)^2 + (-26.627)^2)

Displacement ≈ √(361.452 + 708.048)

Displacement ≈ √1069.5

Displacement ≈ 32.72 m (rounded to two decimal places)

So, the displacement from Jill to Jack at this point is approximately 32.72 meters.