A 700kg rocket is launched from rest with thrust of 9250n, assuming theirs not friction how high, h, is it when it it going 30m/s

Question

matt101 · Answer

If you mean 9250 newtons, all you need to do is first find the acceleration of the rocket, then use that to find height. However, keep in mind that 9250 is NOT the net force. You need to remember the weight of the rocket also plays a role. For the weight of the rocket, or force of gravity, F(g), on the rocket:

$$F=ma$$$$F=700(9.8)$$$$F=6860$$
The weight of the rocket is 6860 N. This opposes the force of the thrust, meaning the net force is 9250-6860=2390 N in the upward direction. Now we can use this net force to calculate the acceleration of the rocket:

$$F=ma$$$$2390=700a$$$$a=3.4$$
So our acceleration is 3.4 m/s^2. We know final velocity, v(f), is 30 m/s. Although it doesn't say in the question, we also know initial velocity, v(i) must be 0 m/s (the rocket starts from rest). We have a, v(f), and v(i), so using this information we can calculate h as follows:

$$v_f^2=v_i^2+2ah$$$$30^2=0^2+2(3.4)h$$$$h=132.4$$
Therefore, the rocket will be travelling at 30 m/s at a height of 132.4 m. Does that make sense? If you have any questions please ask!