A soccer ball is kicked 6m north. then a teamate kicks is 3m east into the goal. what is the soccer balls displacement from where it was first kicked
9 m Northeast
3 m Northeast
-3 m Northeast
6.7 m Northeast
To find the soccer ball's displacement, we can use the Pythagorean theorem.
The distance kicked north is 6m, while the distance kicked east is 3m.
Using the Pythagorean theorem:
Displacement = √(6^2 + 3^2)
Displacement = √(36 + 9)
Displacement = √45
Displacement ≈ 6.7m
Therefore, the soccer ball's displacement from where it was first kicked is approximately 6.7m northeast.
To find the soccer ball's displacement from where it was first kicked, we can use the Pythagorean theorem as both kicks are at right angles to each other.
The first kick of 6m north can be considered as a vertical movement (vertically upwards). The second kick of 3m east can be considered as a horizontal movement (horizontally to the right).
We can form a right-angled triangle with the first kick as the vertical side (6m) and the second kick as the horizontal side (3m). The displacement of the soccer ball will be the hypotenuse of this triangle.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the two sides and c is the length of the hypotenuse, we can calculate the displacement.
Displacement^2 = 6^2 + 3^2
Displacement^2 = 36 + 9
Displacement^2 = 45
Taking the square root of both sides, we find:
Displacement = √45 ≈ 6.7m
Therefore, the soccer ball's displacement from where it was first kicked is approximately 6.7m northeast.
To find the displacement of the soccer ball, we need to find the resultant vector of the two kicks.
First, let's break down the kicks into their respective north and east components:
- The first kick of 6m north gives us a displacement of (0m north, 6m north).
- The second kick of 3m east gives us a displacement of (3m east, 0m north).
Now, let's add the north and east components separately to find the resultant displacement:
North component: 6m north + 0m north = 6m north.
East component: 0m east + 3m east = 3m east.
Therefore, the resultant displacement of the soccer ball is (3m east, 6m north), which is equivalent to 9m northeast.
So, the correct answer is 9m northeast.