College Physics
posted by Phillip .
An artificial satellite is moving in a circular orbit with a speed of 6.5 km/s and a period of 80.0 min. A retarding rocket fires in a direction opposite to the motion. This provides a retarding deceleration of 21.0 m/s2. What is the acute angle between the radius vector and the total acceleration of the satellite?

you have two acceleation vectors.
One is gravity.
Two is the rocket firing
Both of those is at 90 degrees, so the angle can be found from the tangent when adding those.
Gravity: v^2/r
you are given v (convert to m/s), but r can be found from
v^2/r=g(re/r)^2
or r=g*(rearth/v)^2
gravity acceleration= v^2/g(re/v)^2
figure that out, it is pointed down. Check my math.
Radial acceleration: 21m/s^2
angle= arctan (radial acceleration/gravityacceleration)
check all this , I did it in my head. 
bobpursley's answer is wrong. The question isn't a satellite revolving earth anyways.

Total Acceleration will consist of Centripetal (which is in the same direction as the r vector) and Tangential (which at any given moment will be your retarding one. With that we can set up a triangle that gives us the angle needed.
Since we don't know radius we can use V=r2Pi/T and solve for Centripetal.
We get V2Pi/T= Ac. From Ac=V^2/r and using our solve for r from above.
Our answer will be arctan( Aretarding/Ac):
arctan(21/(V2Pi/T))=67.96deg