Question

two forces p and Q are such that the sum of their magnitude is 45 Newtons.the resultant of p and q is perpendicular to p and has a magnitude of 15N .calculate the magnitude of p and of q​

Answer 1

Answer:

P= 20 NEWTON            Q= 25 NEWTON

Explanation:

P + Q = 45     (1)                R= 15              R ⊥ P

Acc. to Parallelogram law,

R² = P² + Q² + 2PQ cosФ

15² = P² + Q² + 2PQ COSФ

25= P² + Q² + 2PQ COSФ                               (2)

Now, R⊥P

tan ∝ = QsinФ/ P + Q cosФ

tan 90° = QsinФ/ P + Q cosФ

∞ = QsinФ/ P + Q cosФ                   (tan 90 is undefined)

∴ P + Q cosФ = 0

∴ -P = Q cosФ                      (2)

Putting value of (3) in equation (2)

225 = P² + Q² + 2P (Q cosФ)

225 = P² + Q² + 2P (-P)

225 = P² + Q² - 2P²

225 = Q² - P²

225 = (Q + P) (Q - P)        

225= (45) ( Q - P)                          ∵ Q + P = 45

Q- P = 225/45

Q- P = 5                                                       (4)            

Adding (1) and (2)

Q + P + Q - P = 45 + 5

2Q = 50

Q = 25  N                                                    (5)

P = 45 - Q                                     FROM (1) AND (5)

P = 45 - 25

P = 20  N