Emily passes a soccer ball 7.1 m directly
across the field to Kara, who then kicks the
ball 13.7 m directly down the field to Luisa.
What is the magnitude of the ball’s total
displacement as it travels between Emily and
Luisa?
Answer in units of m
Howmany degrees to the side of straight down
the field is the ball’s total displacement?
Answer in units of �
UCKF put the f in front
6.6
To find the magnitude of the ball's total displacement, we can use the Pythagorean theorem since the displacements of Emily and Kara are perpendicular to each other. 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.
So, using the given displacements of 7.1 m and 13.7 m, we can calculate the magnitude of the total displacement as follows:
Magnitude of total displacement = √(7.1^2 + 13.7^2)
Magnitude of total displacement = √(50.41 + 187.69)
Magnitude of total displacement = √238.1
Magnitude of total displacement ≈ 15.43 m
Therefore, the magnitude of the ball's total displacement is approximately 15.43 m.
Now, let's calculate how many degrees to the side of straight down the field the ball's total displacement is.
We can use trigonometric functions to find the angle. Since we have the lengths of two sides of a right triangle (vertical and horizontal displacements), we can use the tangent function to find the angle.
Tangent(angle) = Opposite side / Adjacent side
In this case, the opposite side is the vertical displacement (13.7 m), and the adjacent side is the horizontal displacement (7.1 m). Let's calculate:
Tangent(angle) = 13.7 / 7.1
angle = arctan(13.7 / 7.1)
Using a calculator or a specialized function for arctangent, we find that:
angle ≈ 62.6 degrees
Therefore, the ball's total displacement is approximately 62.6 degrees to the side of straight down the field.