a cyclist travels 2.5km east, then 10km south and finally 5km west. determine the cyclist's overall displacement from their starting point.
west = 2.5 km
south = 10 km
magnitude = sqrt(6.25 +100)
tan of angle south of west = 10/2.5 = 4
angle south of west = 76 degrees south of west
To determine the cyclist's overall displacement, we need to consider both the distance traveled and the direction.
First, let's break down the displacements into their respective components:
- East: +2.5 km (positive in the east direction)
- South: -10 km (negative in the south direction)
- West: -5 km (negative in the west direction)
Now, let's add up the displacements to find the overall displacement:
2.5 km (east) + (-10 km) (south) + (-5 km) (west)
Combining the displacements:
2.5 km - 10 km - 5 km
Simplifying the equation:
-10 km - 5 km = -15 km
Therefore, the cyclist's overall displacement from their starting point is 15 km to the west.
To determine the cyclist's overall displacement, we need to find the vector sum of all the individual displacements.
Step 1: Assign a positive direction for each measurement. Let's consider east as positive, south as negative, and west as negative as well.
Step 2: Calculate the individual displacements.
- The cyclist travels 2.5 km east. Since this is the positive direction, the displacement is +2.5 km east.
- Then, the cyclist travels 10 km south. Since this is the negative direction, the displacement is -10 km south.
- Finally, the cyclist travels 5 km west. Since this is also the negative direction, the displacement is -5 km west.
Step 3: Add up all the individual displacements to find the overall displacement.
+2.5 km east + (-10 km south) + (-5 km west)
To add these displacements, we consider their directions. East is positive, so we add 2.5 km. South is negative, so we subtract 10 km. West is also negative, so we subtract 5 km.
2.5 km - 10 km - 5 km = -12.5 km
The overall displacement of the cyclist from their starting point is -12.5 km.