Final answer:
The angle between the resultant and force Q will remain at 90 degrees when force P is doubled, because the increase in P does not affect the original perpendicular relationship between P and Q.
Step-by-step explanation:
The question deals with the resultant of two forces and how this resultant changes when one of the forces is altered. The original resultant has a magnitude equal to that of force P, and when P is doubled, we need to determine the new angle between the resultant and force Q.
To solve this, consider the vector addition of forces P and Q. Initially, when the resultant is equal in magnitude to P, this implies that Q must be at right angles to P (as the components along P's direction would be P, and those perpendicular would be Q, leading to a resultant of magnitude P). Now, when we double P, Q remains perpendicular to P, hence the resultant now forms the hypotenuse of a right-angled triangle with sides of lengths 2P and Q. By definition, the angle between Q and the resultant will still be 90 degrees, because Q remains unaffected and still acts at a right angle to P.