This question refers to my question that was replied to:

Sue and Jenny kick a soccer ball at exactly the same time.Sue's foot exerts a force of 62.3 N to the north. Jenny's foot exerts a force of 115.9 N to the east. What is the magnitude of the resultant force on the ball? Answer in N.

What is the direction of the resultant force (measured from the east)? Answer in degrees

This is what i did, but im not sure if my method is correct.:

squareroot of 62.3^2 + 115.9^2=131.6N

tan^-1 62.3/115.9=28.25 degrees

my degrees were right, but is what i did to find the magnitude of the force on the ball right?

3 answers

Yes, I also get 131.6 N

thanks so much!!

Yes, your method to find the magnitude of the resultant force on the ball is correct.

To find the magnitude of the resultant force, you can use the Pythagorean theorem. Since the forces are perpendicular to each other (north and east), they can be treated as the sides of a right triangle, where the resultant force is the hypotenuse.

Using the Pythagorean theorem, the magnitude of the resultant force can be calculated as the square root of the sum of the squares of the two forces:

Resultant force = √(62.3^2 + 115.9^2) = √(3886.29 + 13486.81) = √(17373.1) ≈ 131.6 N

So your calculation of the magnitude of the resultant force is correct.

Now, to find the direction of the resultant force measured from the east, you can use trigonometric functions.

The direction can be found using the tangent function, as you correctly used it:

Direction = tan^(-1)(62.3/115.9) ≈ 28.25 degrees

So your calculation of the direction of the resultant force is also correct.

Therefore, the magnitude of the resultant force on the ball is approximately 131.6 N, and the direction of the resultant force measured from the east is approximately 28.25 degrees.