How Do You Calculate Displacement and Distance in Physics Problems?

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To calculate displacement and distance in physics problems, it's essential to convert movements into Cartesian coordinates. In the first scenario, the roller coaster's movements were translated into coordinates, allowing for the application of the Pythagorean theorem to find displacement. For the second problem involving polar coordinates, the distance between points was determined by subtracting coordinates and using the distance formula. Drawing diagrams and visualizing the vectors can simplify understanding and calculations. Overall, applying geometric principles and trigonometry can effectively solve these types of physics problems.
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Hi, I have a two questions that I am trying to figure out. If you can help me, that would be great.

1. A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30 above the horizontal. Next, it travels 135 ft at an angle of 40 below the horizontal. Find the roller coaster's displacement from its starting point to the end of this movement.

2. Two points are given in polar coordinates by (r, angle) = (2.00m, 50.0 angle), 2nd one is (5.00, -50 angle), respectively. What is the distance between them?

Thank you ahead of time.
 
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Forum rules state you must show some effort on solving the problem before you can receive help. So show us what you've tried so far and explain what is confusing you. Then we can help you out.

Have you drawn a good diagram? Start with that.
 
Hi, thanks for the reply. For the number one, I actually converted it Cartesian coordinates and drew out a diagram. First set of point, I got (1.29, 1.53) and the r = is 2.00. The 2nd set of polar coordination after the conversion is (3.21, -3.83) and r = 5.00. I actually got the answer by subtracting the first set of coordinate from the 2nd one and use the Pythagorean theoream but I don't understand how that actually work. Hope you can understand what I am trying to say.

As for the 2nd set of problem, I drew everything out and also find out the coordinates with the same method and try to add them all together. For some reason, the sum of the X axis of all the vectors is the answer, which also confused me.
 
I actually got the answer by subtracting the first set of coordinate from the 2nd one and use the Pythagorean theoream but I don't understand how that actually work. Hope you can understand what I am trying to say.
That's one way to do it. You basically just applied the distance formula from geometry. You could also just have draw a line connecting the points making a triangle and then used trig to find the length (this skips the converting part).
As for the 2nd set of problem, I drew everything out and also find out the coordinates with the same method and try to add them all together. For some reason, the sum of the X axis of all the vectors is the answer, which also confused me.
I'm not sure I follow that. You could also do this problem with trig.
 

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