Respuesta :
Explanation:
It is given that,
The angle between the two ropes, [tex]\theta=57^{\circ}[/tex]
Force exerted by dog A, [tex]F_A=280\ N[/tex]
Force exerted by dog B, [tex]F_B=340\ N[/tex]
(a) Let F is the magnitude of the resultant force. It can be calculated as :
[tex]F=\sqrt{F_A^2+F_B^2+2F_AF_B\ cos\theta}[/tex]
[tex]F=\sqrt{(280)^2+(340)^2+2(340)(280)\ cos(57)}[/tex]
F = 545.61 N
(b) Let [tex]\phi[/tex] is the angle the resultant force makes with dog A's rope.
[tex]\phi=tan^{-1}(\dfrac{F_B\ sin\theta}{F_A+F_B\ cos\theta})[/tex]
[tex]\phi=tan^{-1}(\dfrac{340\ sin(57)}{340+280\ cos(57)})[/tex]
[tex]\phi=30.07^{\circ}[/tex]
Hence, this is the required solution.
