What is the acceleration of the 1000 kg boat?

[atse1900]

A boat moves through the water with two forces acting on it. One is a 2000 N motor, and the o ther is an 1800 N restive force to the water. 1) What is the accelration of the 1000 kg boat?

Did I do this right?

a) (2000 cos 90 + 1800 cos 270 ) i + (2000 sin 90 + 1800 sin 270)j = 3800j N

sqrt(3800^2+0^2)= 3800 N.

a= 3800/1000 = 3.8 m/s^2

 

[durt]

The net force is 200 N forward. What are you doing with vectors? That's making this way more complicated than it really is.

 

[franznietzsche]

A boat moves through the water with two forces acting on it. One is a 2000 N motor, and the o ther is an 1800 N restive force to the water. 1) What is the accelration of the 1000 kg boat?
Did I do this right?
a) (2000 cos 90 + 1800 cos 270 ) i + (2000 sin 90 + 1800 sin 270)j = 3800j N
sqrt(3800^2+0^2)= 3800 N.
a= 3800/1000 = 3.8 m/s^2

As durt pointed out you made this far more complicated than necessary. Also, the way you are trying to use vectors seems unnecessarily complicated, however it should have worked. Your mistake was that sin 270 = -1, not 1. Fix that and you'll get the right answer.

It looks like you are just using a cookbook method given to you by your teacher (well, that's the only reason i can think of to intentionally make it that complicated). It will always work (if you take the sines and cosines correctly) but in this case its just more work than necessary. In this case you have two opposing forces, since one is opposite direction change the sign. Since both are at the same angle, just add them directly. Much simpler.

 

[civil_dude]

Always draw a picture. It helps tremendously.