Part B

As shown, two blocks, resting on different inclines, are connected by an inelastic cable that passes over a frictionless pulley. Block $A$

weighs $18\mathrm{.}0$ lb and block $B$ weighs $47\mathrm{.}0$ lb $.$ The incline angles are ${}_1=20\mathrm{.}0$ degrees and ${}_2=65\mathrm{.}0$ degrees, and the coefficient of kinetic friction between the blocks and the inclines is ${}_k=0\mathrm{.}100.$ When the blocks are released from rest, block $B$ slides down its incline. What is the magnitude of block $A\text{'}$s velocity, $v_A,$ after block $B$ has slid $7\mathrm{.}70$ ft $?$

Express your answer to three significant figures and include the appropriate units.