Practice at Home

$7.$ A small remotely controlled robotic vehicle is shown below. The $200-$m tether has a slight negative buoyancy in that a net downward force of $0\mathrm{.}025$ N per meter of its length acts on it$.$ Using its onboard variable horizontal and vertical thrusters, the vehicle maintains the constant $10-$m depth as it moves slowly to the right. If the maximum horizontal thrust is $10$ N and the maximum vertical thrust is $7$ N $,$ determine the maximum permissible value of the distance $d$ and state which thruster is the limiting one.