Mechanics — Variant 2

A block $A$ of mass $80$ kg is connected by a light, inextensible rope to a block $B$ of mass $40$ kg. The rope joining the two blocks is taut and is parallel to a line of greatest slope of a plane which is inclined at an angle of $20^\circ$ to the horizontal. A force of magnitude $500$ N inclined at an angle of $15^\circ$ above the same line of greatest slope acts on $A$ (see diagram). The blocks move up the plane and there is a resistance force of $50$ N on $B$, but no resistance force on $A$.

Find the acceleration of the blocks and the tension in the rope.

Find the time that it takes for the blocks to reach a speed of $1.2$ $\text{m\,s}^{-1}$ from rest.