$6\mathrm{.}25$ A $16-$ft ladder weighing $62$ lb $($assumed concentrated at its midlength$)$ rests on a horisontal floor and is supported by a vertical wall, as shown. The lower end is prevented from slipping by friction and by a rope attached to the base of the wall. The ladder supports a $200-1b$ person at the top. The coefficient of static friction at the wall is $0\mathrm{.}25$ ; at the floer it is $0\mathrm{.}30.$ Calculate the tension $P$ in the rope necessary to prevent slipping.