Question

Two soccer players kick the ball at exactly the same time. One players's foot exettys a force of 60 N north. The other's foot exerts a force of 80 N east. What is the magnitude and direction of the resulatant force on the ball?

Answer 1

Here two vectors (forces) acting along Y direction of F1 = 60 N (North)

and second force F2 = 80 N acting along X dirction (East)

the resultant of the two vectors is

we know that the x component of the vector along y axis is zero and

y component of the vector alon x axis is zero

so writing the vectors in the component form

F1 = F1x i + F1y j ; F2 = F2x i + F2y j

F1 = F1 cos 90 i + F1 sin 90 j ; F2 = F2cos 0 i + F2 sin 0 j

substituting the values of F1,F2

F1 = 60 cos90 i + 60 sin 90 j ; F2 = 80 cos0 i + 80 sin 0 j

F1 = 0 N i + 60 N j ; F2 = 80 N i + 0 N j

the resultant is F = Fx i + Fy j = (F1x+F2x) i +(F1y+F2y) j

F = (0+80)N i + (60 + 0)N j = 80 N i + 60 N j

magnitude is F = sqrt( 80^2+60^2) N = 100 N

direction is theta = arc tan (Fy/Fx) = arc tan (60/80) = 36.87 degrees

so the resultant force on the ball is F = 100N at an angle of 36.87 degrees with X axis