Question

• ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements.

During a treasure hunt, Cody walks 45.0 m south and 7.50 m to the west. What single straight-line displacement could
Cody have taken to reach the treasure? (Remember that magnitude and angle and direction are all needed for your
answer)

Answer 1

45.6 m at
`80.5^(\circ)` south of west

Step-by-step explanation:

Let's take the north-south direction as y-direction (with south being positive) and east-west direction as x-direction (with west being positive). Therefore, the two components of Cody's motion are:

-
`d_y = 45.0 m` (south)

-
`d_x = 7.50 m` (west)

Since they are perpendicular, the magnitude of the net displacement can be calculated by using Pythagorean's theorem:

`d=√(d_x^2+d_y^2)=√(7.50^2+45.0^2)=45.6 m`

The direction instead can be measured as follows:

`\theta = tan^(-1) ((d_y)/(d_x))=tan^(-1)((45.0)/(7.50))=80.5^(\circ)`

And given the convention we have used, this angle is measured as south of west.