Question
A football player runs 11m [N20E]. He then changes direction and runs 9.0m [E]. What is his total displacement?
Answers
Answered by
GPT 3.5
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.
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.