Answer:
Tension in each cable is 3474 N when angle made by the string with horizontal 46 degree
Tension in each cable is 4852 N when angle made by the string with horizontal 31 degree
Explanation:
In this problem, for the boat to be at rest then tension in the strings must be such that the horizontal components balance each other and the vertical components balance weight of the boat.
Consider horizontal components for equilibrium
If the angle made by the string with horizontal 46 degree
[tex]T_{1} cos\theta=T_{2} cos\theta\\T_{1}=T_{2[/tex]
Tension the each string is same
Consider vertical components for equilibrium
[tex]T_{1} sin\theta+T_{2} sin\theta=mg\\\\T_{1} sin46+T_{2} sin46=510 \times 9.8\\\\2T_{1}sin46=4998............(here T_{1}=T_{2})\\T_{1}=3474.01 N[/tex]
Tension in each cable is 3474 N when angle made by the string with horizontal 46 degree
If the angle made by the string with horizontal 31 degree, then
[tex]T_{1} sin\theta+T_{2} sin\theta=mg\\\\T_{1} sin31+T_{2} sin31=510 \times 9.8\\\\2T_{1}sin31=4998............(here T_{1}=T_{2})\\T_{1}=4852.06 N[/tex]
Tension in each cable is 4852 N when angle made by the string with horizontal 31 degree
