A boy runs 20m due north then walks 15m at 60 degree south of east what is his displacement
To find the displacement of the boy, we need to calculate the resultant displacement vector which is the vector sum of the two individual displacements.
First, let's represent the two displacements as vectors:
1. The first displacement of the boy, running 20m due north, can be represented as a vector: 20m North.
2. The second displacement of the boy, walking 15m at 60 degrees south of east, can be represented as a vector: 15m at 60° S of E.
Now, we need to break the second vector into its x and y components:
The x-component = 15m * cos(60°) = 7.5m (positive, to the right)
The y-component = -15m * sin(60°) = -12.99m (negative, downwards)
Note that we use the negative sign for the y-component as it's pointing downwards.
Now, add the x and y components of both vectors separately:
For the x-components: 0m (since the first displacement was in the north direction)
For the y-components: 20m + (-12.99m) = 7.01m
So, the resultant displacement vector is 0m (x-component) + 7.01m (y-component).
Therefore, the boy's displacement is 7.01m upward (north) from his starting position.