Gravitation Help: Calculating Attractive Force & Velocity

[Meowzers]

I'm having trouble distinguishing the values of the components in the gravitation equation for the following problem:

The magnitude of the attractive force of gravity between two bodies is F = GMm/r^2. G is a constant equal to 6.67×10^−11 N·m2/kg2, M and m are the masses, and r is the distance between the centers of the two bodies. The gravitational force of a star of mass 1.14×10^32 kg and radius 3.48×10^9 m is the sole force acting on a rocket of mass 1.25×10^6 kg. The rocket is stationary relative to the star at distance of 1.85×10^11 m. Sadly, the rocket has exhausted its fuel, and it will be pulled to its doom inside the star. How fast will it be moving when it reaches the surface of the star?

Here is how I approached it -

The equations I will be using are:
F = G*M*m/r^2
W=KE
$$KE=\frac{1}{2}m v^2$$

So first off, I solved for the force using the gravitation equation -
G constant = 6.67e-11 Nm^2/kg^2
M (of star) = 1.14*10^32 kg
m (of rocket) = 1.25*10^6 kg
r = now this is where my question is. The problem says that r is the distance between the centers of the two bodies. So, I assumed that it's the radius given 3.48*10^9 m added to the distance between the rocket and the star (1.85*10^11 m) and then squared. Is this correct? Or is it just supposed to be the radius of the star squared?

After that first assumption, I plugged the force value I found into
$$W=F*cos(\theta)(delta x)$$
which brings me to the second question. Is the delta x value = 1.85*10^11 m?

Then, I plugged that value I found for W into $$KE=\frac{1}{2}m v^2$$, where m=1.25*10^6.

Is this a correct approach and did I assume anything wrong?

Thanks in advance!

 

[andrevdh]

The gravitational force is a function of r. Which means that you need to integrate in order to find the work done by this force on the rocket in pulling it towards the star.