Final answer:
The resultant force is the hypotenuse because it represents the net force acting on an object, which is the vector sum of all the forces, and, according to Newton's second law, determines the acceleration of the object.
Step-by-step explanation:
The reason the resultant force is the hypotenuse is because it represents the net force acting on an object. This is the vector sum of all the forces and provides the direction and magnitude of the total force. When two forces are applied at right angles to each other, as in the case of forces F1 (30.0 N) and F2 (40.0 N), the net force (Fnet) can be calculated using the Pythagorean theorem. The magnitude of Fnet is found by taking the square root of the sum of the squares of the components, which gives us Fnet = |(30.0 N)2 + (40.0 N)2| = 50.0 N.
Considering Newton's second law of motion, the acceleration of an object is directly proportional to and in the same direction as the net force acting on it, which in the case of vectors, is represented by the resultant or hypotenuse of the triangle formed by the vector components. Since the hypotenuse is the longest side of a right triangle and also represents the largest force in this context, it is appropriate to consider it as the resultant vector in a force diagram. It combines both magnitude and direction, which are critical in determining the motion of an object.