A car travels 36 km north then 25 km east and then 25 km west, with respect to the starting position what is the car's displacement
Disp. = 36i + 25 - 25 = 36i = 36 km N.
To find the car's displacement with respect to the starting position, we can use the Pythagorean theorem. Displacement is a vector quantity, so we need to consider both the magnitude and direction.
Step 1: Draw a diagram
Start by drawing a coordinate system. Place the starting position at the origin (0,0). Since the car travels north first, draw a vertical line 36 km above the origin. Then, from the endpoint of this line, draw a horizontal line 25 km to the right and another 25 km to the left.
Your diagram should look like this:
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25 km to the right
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25 km to the left
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v
0 km
Step 2: Calculate the magnitude
We can see that the car moved 36 km north and ended up 0 km to the north-south direction. The horizontal motion cancels out since the car traveled 25 km to the right and 25 km to the left. Therefore, the car's displacement is only in the north-south direction, with a magnitude of 36 km.
Step 3: Determine the direction
Since the car traveled north, the displacement is positive in the north direction.
So, the car's displacement with respect to the starting position is 36 km north.