Question

While playing a scavenger hunt game, Anthony walks 48.0 m to the south and then walks 12.0 m to the west. What single straight-line displacement could Anthony have taken to reach this point? (Use trigonometry to answer, but remember to draw a diagram to help your understanding.) Give both the magnitude and the angle in your answer.

Answer options
-49.5 m and 14° west of south
-60.0 m and 76° west of south
-49.5 m and 14° southwest
-49.5 m and 12° southwest

Answer 1

Option -40.5 m and 14 west of south is correct

Answer 2

-49.5 m and 14° southwest

Step-by-step explanation:

In order to solve this you first have to remember the rules of trigonometry, so you know that in any right triangle the summ of its squared sides it´s equal to the hypotenuse squared. So we first calculate the magnitude of the hypotenuse:

`h^(2) =ad^(2) +opp^(2)`

The adjacent would be the Y vector, it´s important to knoe where is the location of our angle to be able to properly calculate its dimensions later, and the opposite will be the X vector:

`h^(2) =48^(2) +12^(2)`

`h^(2) =2304 +144`

`h=√(2304+144)\\ h=√(2448)\\h=49.47`

Now we know that the vector is 49.5 rounded.

To calculate the angle we just have trigonometry, and as we know the value of all the sides we can use inverse sine of opp/hyp:

`inverse sine(12)/(49.5) \\inverse sine.2424`

Inverse sine=14.04º

So since the angle that we chose is departing from the Y axis, and into the left of the graph, we now that it is south, and west, so the magnitude is -49.5 m 14º south west.