A cyclist travel 2.5km east then 10.0km south and finally 5.0km west.Determine thecyclistcyclist's overall displacement from their starting point.
total west = 5 - 2.5 = 2.5
total south =10
total magnitude = sqrt (10^2 + 2.5)^2
tangent of angle west of south = 2.5/10 = .25
you have to convert the tangentTheta to a direction.
Disp. = 2.5 - 10i - 5 = -2.5 - 10i = 10.31km[76o] S. of W. = 10.31km[256o] CCW from+x-axis.
Tan A = Y/X = (-10)/(-2.5).
To determine the cyclist's overall displacement, we will use vector addition. First, let's break down the given distances into their x and y components.
- 2.5km east has an x-component of +2.5km and a y-component of 0km (since it is in the east direction).
- 10.0km south has an x-component of 0km (since it is in the south direction) and a y-component of -10.0km.
- 5.0km west has an x-component of -5.0km and a y-component of 0km (since it is in the west direction).
Now, we can add up the x-components and the y-components separately to get the total displacement in each direction.
Adding the x-components: +2.5km + (-5.0km) = -2.5km
Adding the y-components: 0km + (-10.0km) = -10.0km
The total displacement is (-2.5km, -10.0km), which means the cyclist's overall displacement from their starting point is 2.5km west and 10.0km south.