two people kick a ball. one of them kicks it with a force of 215.0 newtons. the other one with 189.0 newtons. their approach creates a 210.0 degree angle at the point of impact and causes the ball to go in a different direction. what is the resultant of the vector from this impact?

i got 107.5365772 newtons. is this correct?

magnitude^2=215^2+189^2-2*215*210*cos(30degrees)=61^2N

81,946 - 90,300*cos(30degrees) = 61^2 N

3,743.9 = 61^2 N

3,743.9 = 3,721 N

1.006 = N

was i suppose to solve it out like that?

Hardly.

if
magnitude^2=61^2
then magnitude is 61N

To find the resultant of the vector from the impact, we need to use vector addition. This involves breaking down the forces into their horizontal and vertical components and then adding them together.

Let's first find the horizontal components of the forces. To do this, we multiply the magnitude of each force by the cosine of the angle it makes with the horizontal axis:

Horizontal component of the first force = 215.0 N * cos(210.0°)
Horizontal component of the second force = 189.0 N * cos(210.0°)

Next, let's find the vertical components of the forces. We multiply the magnitude of each force by the sine of the angle it makes with the vertical axis:

Vertical component of the first force = 215.0 N * sin(210.0°)
Vertical component of the second force = 189.0 N * sin(210.0°)

Now, add up the horizontal components and the vertical components separately:

Resultant horizontal component = (sum of horizontal components)
Resultant vertical component = (sum of vertical components)

Finally, to find the magnitude of the resultant vector, use the Pythagorean theorem:

Resultant magnitude = sqrt((Resultant horizontal component)^2 + (Resultant vertical component)^2)

To check if your answer of 107.5365772 N is correct, you can plug in the given values and calculate the resultant magnitude.