Question

Two objects of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley. The 5.00kg object lies on a smooth incline of angle 40 degrees. Find the accelerations of each object and the tension in the string.

Work:
(10kg)(9.8m/s^2)(sin40)-T=10a
a=4.20m/s^2
T=5a
T=21N

However, the answer is 4.43m/s^2 and 204N.

Answer 1

No.
The pulling force is 5*anglefunction*g
the angle function is either sin or cosine, I don't know how the 40 deg was measured. If it was measured from the vertical, then it is Cosine.
Then
Pulling force = total mass *a

where total mass is 15kg

Answer 2

, or



Then, Equation (1) yields