A car travels 59.5 miles at 53.0° S of W. The car then makes a 90.0° turn to the left and travels an additional 90.3 miles. What is the car's final displacement?

Question

I have set up the diagram, and I believe I am supposed to use the pythagorean theorem.

Well let me reverse that, I can use the pythagorean theorem because 59.5 m and 93.0 m was given to me, but I was also given an angle 53°. Honestly I'm not exactly sure how to approach this question. BUT I do believe I made my diagram correctly which I put on pasteboard( nevermind I am not allowed to post links )

Answer 1

well, this was what I decided to go with.

since it has designated that he made a 90° turn; We can indicate that it is a right triangle. So, I performed this:

√( (59.5)^2 + (93.0)^2 )

Answer 2

Whoops sorry forgot to give my value after doing the calculation. My answer is: 110.4 miles, the miles squared gets square rooted so then it becomes just miles, right?

Answer 3

Remember it did not just ask for distance (scalar) but also direction (vector).

Answer 4

But good job so far Hanky.

Answer 5

Ok, so I am guessing I need to use the angle given to me. Now I have to find the hypotenuse length and angle? I think?

Answer 6

the angle counterclockwise from west is 53 + tan^-1(90.3/59.5)

that will end up in quadrant 4, east of south

Answer 7

53 + 56.6 counterclockwise from west
or 109.6
which is 109.6 - 90 = 19.6 degrees east of South

Answer 8

if I did it my way, would I be taking steps to solve the problem?

Answer 9

or actually that is what you said, sorry.

Answer 10

I thought I did it your way :)
All I did was get the angle, you got the distance (hypotenuse)

Answer 11

Ok thank you!

I accidentally miscalculated my hypotenuse... so now my final answer is:
108.14 miles 56.6°East of South, because it passes the third quadrant by 19.6° which is why you subtracted 90°