A car heads due west on Interstate 80 going 63.0 km/hr for 2.1 hours. The car then turns and heads exactly northwest on Interstate 42 going 53 km/hr for 3.3 hours. What is the resultant displacement of the car?

I've done some work on it and I have a good idea. I found the total distance traveled for each direction, which is 63 * 2.1 = 132.3km for the first and 53 * 3.3 = 174.9km for the second.

Northwest = 45 degrees

Then, the cos(45)*174.9 = 123.67. That must be the length of each of the sides for the triangle with 174.9 as its hypotenuse.

Finally, the total bottom distance must be 132.3 + 123.67 =255.97

sqrt of 255.97^2 + 123.67^2 = 284.28 km. Is this correct?

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  1. west distance
    = 63*2.1 + 53 (sqrt2/2)*3.3
    = 255.97 right
    north distance
    = 53*(sqrt2/2)*3.3
    = 123.67 right

    so 284.28 is correct for the DISTANCE
    Distance is scalar , km
    Displacement is vector , distance AND direction
    tan (angle north of west) = 124/256
    angle north of west = 25.8 degrees

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  2. Note
    always do orthogonal (perpendicular) components of vectors like x and y or north and west. Do not fool around with northwest, split it up into north component and west component immediately. Otherwise you will be doing trig forever.

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  3. @Damon, just one question. Sorry, but I'm not sure where you got the 124 and 256 from.

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