Question

The resultant of the two forces has a magnitude of 650 lb. Determine the direction of the resultant and the magnitude of P.

Answer 1

Answer:

3000 will be the answer means magnitude of p

Answer 2

Answer:

The magnitude of P vector is 234.76lb and the angle of resulatant vector with P vector is 41.76°

Explanation:

Given are 2 force vectors that are at an angle of 60° with each other and their resultant is 650lb.

Magnitude of first vector=Q=500lb

Magnitude of second vector=P

Resultant of 2 vectors at an angle θ is given by,

$R=\sqrt{P^{2} +Q^{2}+2PQcos\theta }$

On substituting the values,

$650=\sqrt{P^{2} +500^{2}+2\times P\times500\times 0.5 }$

On solving,

P=234.76lb

Direction of resultant vector is given by,

$tan\alpha =\frac{QSin\theta}{A+BCos\theta}$

On substituting the values,

$tan\alpha =\frac{500\times \frac{\sqrt{3} }{2} }{234.76+500\times \frac{1}{2} }$

On solving,

$tan\ \alpha =0.893$

α=41.76°