You can view this as an inelastic collision between a 2000 kg object moving at 3 m/s, and a stationary 500 kg object.
The total momentum of the objects before the collision equals their momentum after collision.
Before:
flatcar = 2000*3 = 6000 kg*m/s.
<span> coal = 0*500 = 0.
After:
flatcar & coal = 2500*V
then
</span> 2500*V <span>= 6000,
V = 2.4 m/s.
</span> Additional:
the definition of an inelastic collision is that the objects "stick together" after colliding.
This problem is going to be pretty long to solve. So, prepare.
We’re interested in the change in our x position. So we have to break the velocity vector up into its components. Do cosine of 50 and then multiply by the magnitude of the velocity. I got 20.57m/s. That’s our initial velocity. And remember, horizontal acceleration is zero. The vertical acceleration, or any vertical component, has no effect on the horizontal components. In order to solve this problem, we want to utilize this equation:
Change in x-position = Vix*t
Let’s solve for time, which is dependent on the vertical components. The projectile will stop when it vertically hits the ground. Generally you want to use this equation for solving for time:
Yf = Yi + Viy*t + 1/2at^2
We didn’t solve for the vertical component yet, so let’s do that now. (Sine of 50)*(32) = 24.51m/s
Let’s now plug everything in:
0 = 0 + 24.5t - 4.9t^2
0 = 24.5t - 4.9t^2
0 = t(24.5 - 4.9t)
-24.5 = -4.9t
t = 5 seconds
The hard stuff is pretty much over. Put that 5 seconds into the other equation I said we wanted to use to solve the problem
Change in x-position (range) = (20.57)*(5)
= 102.85 meters
Answer B
Answer:
a) The module's acceleration in a vertical takeoff from the Moon will be 
b) Then we can say that a thrust of
won't be able to lift off the module from the Earth because it's smaller than the module's weight (
).
Explanation:
a) During a vertical takeoff, the sum of the forces in the vertical axis will be equal to mass times the module's acceleration. In this this case, the thrust of the module's engines and the total module's weight are the only vertical forces. (In the Moon, the module's weight will be equal to its mass times the Moon's gravity acceleration)

Where:
thrust 
module's mass 
moon's gravity acceleration 
module's acceleration during takeoff
Then, we can find the acceleration like this:


The module's acceleration in a vertical takeoff from the Moon will be 
b) To takeoff, the module's engines must generate a thrust bigger than the module's weight, which will be its mass times the Earth's gravity acceleration.

Then we can say that a thrust of
won't be able to lift off the module from the Earth because it's smaller than the module's weight (
).