A soccer ball is kicked 6 m north. Then a teammate kicks it 3 m east into the goal. What is the soccer ball’s DISTANCE.
To find the distance the soccer ball traveled, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the 6 m north and 3 m east movements form a right triangle. We can use the Pythagorean theorem to find the length of the hypotenuse, which will be the distance the soccer ball traveled.
Using the Pythagorean theorem:
Distance^2 = (6 m)^2 + (3 m)^2
Simplifying:
Distance^2 = 36 m^2 + 9 m^2
Distance^2 = 45 m^2
Taking the square root of both sides:
Distance = √(45 m^2)
Distance ≈ 6.71 m
Therefore, the soccer ball's distance is approximately 6.71 meters.
To find the distance traveled by the soccer ball, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the northward kick and the eastward kick form the two sides of the right triangle, and the distance traveled by the soccer ball acts as the hypotenuse. Let's label the northward kick as side A and the eastward kick as side B.
Given that the northward kick is 6 m and eastward kick is 3 m, we can substitute these values into the Pythagorean theorem:
distance^2 = A^2 + B^2
distance^2 = (6 m)^2 + (3 m)^2
distance^2 = 36 m^2 + 9 m^2
distance^2 = 45 m^2
Now, to find the distance traveled by the soccer ball, we take the square root of both sides of the equation:
distance = √(45 m^2)
distance ≈ 6.71 m
Therefore, the soccer ball's distance is approximately 6.71 meters.