Use the forces to find Q

Question

Forces F(40N, 045°) and Q(PN, 135°) act on a body initially at rest. If the magnitude of their resultant is 50N, find the value of P

Answer 1

Break up your two forces into their $x$ and $y$ components. To get the $x$ component, multiply the magnitude of your force by the cosine of your angle, and to get the $y$ component, multiply the magnitude of your force by the sine of your angle.

$F=(F_x)\hat{x}+(F_y)\hat{y}=(40\cos(45^\circ))\hat{x}+(40\sin(45^\circ))\hat{y}$

$Q=(Q_x)\hat{x}+(Q_y)\hat{y}=(P\cos(135^\circ))\hat{x}+(P\sin(135^\circ))\hat{y}$

You know the magnitude of their resultant vector is $50$N, so that means $$50=\sqrt{(F_{x}+Q_{x})^2+(F_{y}+Q_{y})^2}$$

Can you plug in the corresponding values and solve for P?