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?
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 )
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 )
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?
Remember it did not just ask for distance (scalar) but also direction (vector).
But good job so far Hanky.
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?
the angle counterclockwise from west is 53 + tan^-1(90.3/59.5)
that will end up in quadrant 4, east of south
53 + 56.6 counterclockwise from west
or 109.6
which is 109.6 - 90 = 19.6 degrees east of South
if I did it my way, would I be taking steps to solve the problem?
or actually that is what you said, sorry.
I thought I did it your way :)
All I did was get the angle, you got the distance (hypotenuse)