A football player runs 11m [N20E]. He then changes direction and runs 9.0m [E]. What is his total displacement?
To find the total displacement, we can combine the magnitudes and directions of the two runs.
The first run is 11m [N20E]. This means the player ran 11m in a direction 20 degrees east of north.
The second run is 9.0m [E], which means the player ran 9.0m directly east.
To combine the two runs and find the total displacement, we can use vector addition:
First, we convert the directions to cartesian coordinates.
For the first run, the x-component (east-west direction) is given by 11m * cos(20°), and the y-component (north-south direction) is given by 11m * sin(20°).
x-component of the first run = 11m * cos(20°) = 10.22m
y-component of the first run = 11m * sin(20°) = 3.78m
For the second run, since it is directly east, the x-component is 9.0m and the y-component is 0m.
x-component of the second run = 9.0m
y-component of the second run = 0m
Now, we can find the total displacement by adding the x-components and y-components separately.
x-component of total displacement = 10.22m + 9.0m = 19.22m
y-component of total displacement = 3.78m + 0m = 3.78m
Finally, we can find the magnitude and direction of the total displacement using the Pythagorean theorem and trigonometry.
Magnitude of total displacement = sqrt((19.22m)^2 + (3.78m)^2) ≈ 19.67m
Direction of total displacement = atan(y-component/x-component) = atan(3.78m/19.22m) ≈ 11.25°
Therefore, the total displacement of the football player is approximately 19.67m in a direction of 11.25° east of north.