Sue and Jenny kick a soccer ball at exactly the same time. Sues foot exerts a force of 40.6 N to the north. Jennys foot exerts a force of 84.8 N to the east. What is the magnitude of the resultant force on the ball. Answer in units of N.

What is the direction Of the resultant force (measured from the East)?
Answer in units of N.

To find the magnitude of the resultant force on the soccer ball, we can use the concept of vector addition. In this case, we have a force exerted by Sue in the north direction (upwards) and a force exerted by Jenny in the east direction (to the right). These forces can be represented as vectors.

To calculate the magnitude of the resultant force, we can use the Pythagorean theorem. The magnitude of the resultant force, R, is given by the square root of the sum of the squares of the individual forces:

R = sqrt(Sue's force^2 + Jenny's force^2)

R = sqrt(40.6^2 + 84.8^2)

R = sqrt(1651.36 + 7180.64)

R = sqrt(8832)

R ≈ 94.00 N (rounded to two decimal places)

Next, to find the direction of the resultant force measured from the east, we can use trigonometry. We can calculate the angle (θ) using the arctangent function:

θ = arctan(Jenny's force / Sue's force)

θ = arctan(84.8 / 40.6)

θ ≈ arctan(2.0867)

θ ≈ 64.77° (rounded to two decimal places)

So, the magnitude of the resultant force is approximately 94.00 N, and the direction of the resultant force measured from the east is approximately 64.77°.