How Do You Calculate the Acceleration and Distance of a Box Pulled at an Angle?

[lefty1405]

Ive never used this before but my teacher said it worked well.
i guess i just write the problem...
a 50.0 kg box on frictionless wheels is pulled across the floor by a rope with 68 N of tension. The rope makes and angle of 34 degrees to the ground. calculate the acceleration of the box along the floor. If the box starts from rest how far will it have moved after 15.5 seconds?

if you can explain the process or give me any help please let me know or IM me at lefty1405

 

[kevinalm]

First you need to resolve the force vector to it's horizontal (x) and vertical (y) components. (You really only need the horizontal component for this problem) Then F sub x=ma. Finally integrate a twice with respect to t or if you aren't doing calculus yet use the distance formula in your text.

 

[scholzie]

As kevinalm mentioned, your force is a vector, which has components of horizontal and vertical directions. You need to use $$F\sin\theta$$ and $$F\cos\theta$$ to break the total force into its components (I'll leave you up to figuring out which to use for which, though).
After that, it's a simple matter of using $$F=ma$$ and $$x-x_0=v_{0}t+1/2at^2$$ to find the distance.