a soccer ball is kicked 6 m north then a teammate kicks its 3m east into the goal what is the soccer ball displacement from where it was first kicked
To find the displacement of the soccer ball, we can use the Pythagorean theorem because the vectors form a right triangle.
The magnitude of the displacement can be found using the formula:
Displacement = √(x^2 + y^2),
where x represents the horizontal distance and y represents the vertical distance.
In this case, the soccer ball is kicked 6 m north (upward) and then 3 m east (rightward). So, the horizontal distance (x) is 3 m, and the vertical distance (y) is 6 m.
Using the formula,
Displacement = √(3^2 + 6^2)
Displacement = √(9 + 36)
Displacement = √45
Displacement ≈ 6.71 m
Therefore, the soccer ball's displacement from where it was first kicked is approximately 6.71 meters.
To calculate the displacement of the soccer ball from where it was first kicked, we can use the Pythagorean theorem because the displacement forms a right-angled triangle.
First, let's determine the distance traveled in the north direction, which is 6 meters. Next, let's determine the distance traveled in the east direction, which is 3 meters. Now, we can use these distances to calculate the displacement.
Since the north and east directions form a right-angled triangle, we can use the Pythagorean theorem to find the displacement.
The formula for the Pythagorean theorem is:
displacement = √(north^2 + east^2)
Plugging in the values, we get:
displacement = √(6^2 + 3^2)
displacement = √(36 + 9)
displacement = √45
displacement ≈ 6.71 meters
So, the soccer ball's displacement from where it was first kicked is approximately 6.71 meters.
To determine the displacement of the soccer ball, we need to find the resultant displacement by combining the individual displacements in both the north and east directions.
The first kick moves the soccer ball 6 meters to the north. This can be represented as a displacement vector of +6 m in the north direction.
The second kick then moves the soccer ball 3 meters to the east. This can be represented as a displacement vector of +3 m in the east direction.
To find the resultant displacement, we can draw the vectors on a graph and use the Pythagorean theorem to calculate the magnitude of the resultant displacement:
Using the Pythagorean theorem:
Resultant displacement (magnitude) = √(6^2 + 3^2)
= √(36 + 9)
= √45
Therefore, the resultant displacement (magnitude) of the soccer ball is approximately 6.708 meters.
However, we also need to determine the direction of the displacement. To find the direction, we can use trigonometry:
tanθ = opposite / adjacent
tanθ = 6 / 3
θ = tan^(-1)(6 / 3)
θ = tan^(-1)(2)
θ ≈ 63.43°
Therefore, the resultant displacement of the soccer ball is approximately 6.708 meters at an angle of approximately 63.43° from its original position.