A soccer ball is kicked 6m north. then a teamate kicks is 3m east into the goal. what is the soccer balls distance
9 m
3 m
3 m
6.7 m
To find the soccer ball's distance, we need to calculate the magnitude of the displacement vector.
The soccer ball is kicked 6m north. This means that the displacement vector after the first kick is 6m north (in the y-direction).
Then, the teammate kicks the ball 3m east. This means that the displacement vector after the second kick is 3m east (in the x-direction).
To find the total displacement, we can add the two displacements as vectors: (0, 6) + (3, 0) = (3, 6).
To find the magnitude of this displacement vector, we can use the Pythagorean theorem:
Distance = sqrt((3^2) + (6^2)) = sqrt(9 + 36) = sqrt(45) ≈ 6.7m
Therefore, the soccer ball's distance is approximately 6.7m.
To find the soccer ball's total distance, we need to use the Pythagorean theorem because it traveled in a right triangle. The distance traveled north is 6m, and the distance traveled east is 3m.
Using the Pythagorean theorem:
Distance^2 = (6m)^2 + (3m)^2
Distance^2 = 36m^2 + 9m^2
Distance^2 = 45m^2
Taking the square root of both sides:
Distance = √45m^2
Distance ≈ 6.7m
Therefore, the soccer ball's distance is approximately 6.7m.
To find the distance traveled by the soccer ball, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the distance kicked north forms one side of the right triangle, and the distance kicked east forms the other side. So, we can use the formula:
distance = √(north^2 + east^2)
Plugging in the values from the question, we get:
distance = √(6^2 + 3^2)
distance = √(36 + 9)
distance = √45
distance ≈ 6.7 meters
Therefore, the distance traveled by the soccer ball is approximately 6.7 meters.