physics- force question pt 3. please help :)

Question

A child is pulling a 6.8 kg wagon by the handle with a 64 N force. This force is applied through the handle and acts on the wagon at an angle of 35° above horizontal. If the friction force on the wagon is 28.8 N. Calculate the acceleration of the the wagon.

Report your answer:
in terms of m/s2. Do not include units in your answer. They will be assumed to be m/s2.
to a precision of tenths of a m/s2. Use a format like ##.# in your answer.
to an accuracy of 0.2 m/s2. Answers within 0.2 m/s2 of the correct answer will be tolerated.

Answer 1

 

T = force applied through handle = 64 N

θ = angle of applied force relative to horizontal = 35º

m = mass of wagon = 6.8 kg

f = friction force = 28.8 N

 

Assume right is (+) and left is (-).  Find sum of forces in horizontal direction and solve for a:

 

Tcosθ - f = ma

 

a = (Tcosθ - f) / m = [64cos(35º) - 28.8] / (6.8) m/s² = 3.47 m/s²