What is the asteroid's acceleration in unit-vector notation?

[tjcreamer9]

Three astronauts, propelled by jet backpacks, push and guide a 150 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-31.
a 32N vector coming from the origin into the 1st corridor at 30 degrees, 55N straight out to the right and a 41N vector running from the origin to the 4th corridor at 60 degress
Figure 5-31

(a) What is the asteroid's acceleration in unit-vector notation?
m/s2 i + m/s2 j

(b) What is the asteroid's acceleration as a magnitude and direction?
m/s2
° (counterclockwise from the +x axis is positive)


i have tried finding the i and j hat values for each specific vector and then adding and subtracting but i can't seem to get the right answer
27.71i+55i+20.5i= i hat of the asteroid
16j+0j-35.57j= j hat of the asteriod

 

[learningphysics]

what you've written is the force in the x and y directions. did you divide by mass to get acceleration?

 

[Kurdt]

With questions about vectors such as this you are really just using trigonometry. You know the magnitude of the vector and the direction as an angle from whatever axis, therefore you can work out the lengths of the other two sides using trigonometry. The magnitude of the vector will of course be the length of the hypotenuse.