What is the magnitude of the resultant force on the ball?

Question

Sue and Jenny kick a soccer ball at exactly
the same time. Sue's foot exerts a force of
41.7 N to the north. Jenny's foot exerts a
force of 116.3 N to the east.

a) What is the magnitude of the resultant
force on the ball? Answer in units of N.

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

Answer 1

If you draw the vectors in a x-y coordinate system and the tail of these vectors at the origin, then, making North your positive y-axis and east your negative x-axis,

the magnitude is the square root of the sum of the squares of these vectors:

Magnitude F = ( (Fx)^2 + (Fy)^2 )^(1/2)

F = ( (-116.3)^2 + (41.7)^2) ^(1/2)

F = 123.55 N


the angle of the direction would be

angle = arctan (Fy / -Fx)

angle = 19.7 degrees measured from the negative x-axis or east.


I hope this helps, good luck.

Answer 2

a) Magnitude = (ForceN^2 +ForceE^2)^1/2 = 123.55 N
b) Direction = tan inverse (Force N/Force E) = 19.72 degrees measured from east

Answer 3

f=squaredroot [(41.7)^2 + (116.3)^2] = squaredroot [15264.58] = 123.5499089
angle = TAN-1(41.7/123.55) = 19.72557242

Answer 4

part B is actually the inverse of Sin instead of the inverse of tangent