Inclined Plane with pulley

a) An inclined plane making an angle of 25 degree with the horizontal has a pulley at its top. A 30kg block on the plane is connected to a freely hanging 20kg block by means of a cord passing over the pulley. Compute the distance the 20kg block will fall in 2s starting from rest. Neglect friction.

b) Repeat the problem above if the coefficient of friction between block and plane is 0.20.

Answers for (a) is 2.87m and (b) is 0.74m, but I would like to know the detailed work.

a) the tension in the rope is the same throughout;

newton's second law tells us that the sum of forces on a mass = m a

apply newton's second law to the 20kg mass and we have

T - 20 g = - 20 a where a is the accel of the block and is assumed down

for the block on the plane, we have T - 30 g sin 25 = 30a

solve these two equations simultaneously: and get that a = 1.44m/s/s

starting from rest, the distance traveled is dist = 1/2 a t^2

dist = 1/2 x 1.44m/s/s x (2s)^2 = 2.88m

b) if there is friction, newton's second law for the block on the plane becomes

T - 30 g sin 25 - 0.20 x 30 kg x 9.81m/s/s cos 25 = 30 a

in this case, the force of friction acts down the plane since the 30 kg mass moves up the plane (hence has a negative sign) and magnitude
u mg cos(theta)

the equation for the hanging block remains T - 20 g = - 20a

solving simultaneously yields a = 0.37m/s/s

and dist = 1/2 x 0.37m/s/s x (2s)^2 = 0.74m