How Do Astronauts Calculate the Acceleration of an Asteroid in Space?

[Jumpman24]

1.Three astronauts, propelled by jet backpacks, push and guide a 85 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-31.
http://img82.imageshack.us/img82/6572/0539aw6.gif
(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)

2. Homework Equations
W= F * d
3. a) 55/85 m/s2 i + (32 cos 30-40 cos 60)/85 m/s2 j
= 0.65 m/s2 i + 0.091 m/s2 j

b) (.65^2 +.091^2) ^.5 is the net acceleration.
for direction i used tan x=.091/.65
answer= .14i need help

 

[Stovebolt]

The question does not seem to be asking for Work or Energy, so the equation W = F * d does not seem correct.

You do have the right idea in terms of calculating acceleration from the force / mass (a = F / m), but you didn't quite get the procedure correct.

Using unit-vector notation, the i unit vector will be the sum of the forces in the x-direction, and the j unit vector will be the sum of the forces in the y-direction.

Hopefully this will put you on the right track.

 

[Jumpman24]

still confused on which equation to use

 

[Stovebolt]

Looking at your first post, you used F = ma (or a = F/m). You found one component of the i unit vector as 55 N / 85 kg. This was correct.

However, the point where you went wrong was in using
(32 cos 30-40 cos 60)/85 as the j unit vector. The cosine of the angle times the hypotenuse will give you the x-component of each force, which would be part of the i unit vector.