Two people Simultaneously kick the same soccer ball, each with a force of 10. N. One force is directed 45 degrees N of E, the other 30 degrees S of E. What are the magnitude and direction of the resultant of their forces?
I know that for one of them the angle is 30 degrees and one of the legs is 10N. How do I find the Resultant? What formula do I use. Also, the other angel with 45 degrees and a leg measuring 10 N, how do I find the resultant for that? What formula do I use.
Fr = 10N[45o] + 10N[330]
X = 10*Cos45 + 10*Cos330 = 15.73 m/s.
Y = 10*sin45 + 10*sin330 = 2.071 m/s.
Tan A = Y/X = 2.071/15.73 = 0.13166
A = 7.50o.
Fr = X/Cos A = 15.73/Cos7.50 = 15.9 N. @
7.50o.
To find the resultant of two forces, you can use the parallelogram law of vector addition. According to this law, the resultant of two vectors can be found by constructing a parallelogram using the vectors as adjacent sides and drawing the diagonal of the parallelogram.
For the force directed 45 degrees N of E with a magnitude of 10 N, you can break it down into its horizontal and vertical components. The horizontal component can be calculated as: 10 N * cos(45°). Since the force is directed North of East, the vertical component will be in the positive Y direction. The vertical component can be calculated as: 10 N * sin(45°).
Similarly, for the force directed 30 degrees S of E with a magnitude of 10 N, you can break it down into its horizontal and vertical components. The horizontal component can be calculated as: 10 N * cos(30°). Since the force is directed South of East, the vertical component will be in the negative Y direction. The vertical component can be calculated as: -10 N * sin(30°).
Once you have the horizontal and vertical components for both forces, you can add them together to find the resultant. The magnitude of the resultant can be calculated using the Pythagorean theorem: resultant magnitude = √((horizontal component)^2 + (vertical component)^2).
To find the direction of the resultant, you can use the inverse tangent function: direction = atan(vertical component / horizontal component). Make sure to consider the signs of the components when using the inverse tangent function to determine the direction.
By applying these calculations to both forces, you can find the magnitude and direction of the resultant.