Problem: One object has a momentum of 19 kg m/s toward the East and another has momentum 17 kg m/s toward the North. When they collide, the first object is stopped by the impulse of a constant force. What is the angle between the easterly direction and the force exerted by the object on the source of the impulse?
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Solution: Sketch a triangle representing this situation. The triangle will have a vertical leg of 17 Newtons and a horizontal leg of 25.49 Newtons. The hypotenuse represents the total force. The angle of the hypotenuse with East is arctan( 17 / 19) = 41.83 degrees. The magnitude of the force is `sqrt( ( 19) ^ 2 + ( 17) ^ 2) Newtons = 25.49 Newtons.
Generalized Response: Each applied force will tend to influence the motion of the object by tending to accelerate the object in its direction, with the net result depending on the directions and magnitudes of the applied forces. In this case the net effect of the two mutually perpendicular forces will be their vector resultant. This resultant will have magnitude |F| = `sqrt(Fx^2 + Fy^2) and will make angle arctan(Fy / Fx) with the positive x axis.
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Figure description: The figure below depicts the components Fx and Fy of a net force. The magnitude of the net force is represented by the hypotenuse of the triangle, and is equal to `sqrt(Fx^2 + Fy^2). The direction of the force, as measured from the positive x axis, is arctan(Fy / Fx).
