# Thread: Help With A Rocket & Its Velocity / Range

1. ## Help With A Rocket & Its Velocity / Range

Hi, I am new to this forum so please forgive my ignorance and very low standards of maths. I have been given a problem to solve that is just one part of a larger puzzle. Only this small part of the puzzle is mathematical.

The information I have been given is below.

"A rocket is launched. The launch was just off vertical, at an angle of 89.8968°. The rocket reached 174.6km above sea level before crashing back to ground not too far away. I need to know the distance the rocket travelled please. The distance horizontally from point of launch to point of landing.

Further information

* The rocket wasn't guided, nor propelled after take off. It followed the parabolic trajectory of a simple projectile.
* Both the launch point and landing site can be taken to be at sea level.
* Acceleration due to gravity is 9.81 m/s2.
* The effects of air resistance, the earth's rotation, etc., etc., etc. can be ignored."

Thanks in advance to anyone that can help. I would like to say that I have tried and failed with this one but I struggle to even start. I think I would need to know the velocity of the rocket but once again, not a clue where to begin.

Steve

2. ## Re: Help With A Rocket & Its Velocity / Range

equations from physics ...

height, $H = \dfrac{(v_0\sin{\theta})^2}{2g} \implies v_0^2 = \dfrac{2gH}{\sin^2{\theta}}$

range, $R = \dfrac{v_0^2 \sin(2\theta)}{g}$

$v_0$ is initial velocity

$\theta$ is the launch angle relative to the horizontal

$g$ is the magnitude of the acceleration due to gravity at the Earth's surface.

I'd use the height equation to determine $v_0^2$, then sub into the range equation. Watch your units.

3. ## Re: Help With A Rocket & Its Velocity / Range

Many thanks for your time and reply. Unfortunately I am still very much in the dark. My math skills are on a much lower level.

I can see what I need to do but not sure how to go about it. For example, I have no idea what to do with "sin", or what's it's value is. Something in the back of my head says "sine / cosine"
I am presuming that g is 9.81 and H would need to be 1746000 because we are working in meters ?

Also confused how the numbers are dealt with when they are in a small string. Does 2gH mean (2 x g x H) or (2g x H) or (2 gxH)

If I were to attempt this I would say that velocity is (2 x 9.81 x 174600) devided by ("sin?" Squared x 89.8968)
Which would be 3425652 devided by ("sin?" Squared x 89.8968)

I also presume that when you sas "watch your units" you meant I needed to standardise my units across the board and use meters rather than km.

Yes I have seen the "sin" key on the calculator but still in the dark as to what it means and how to "square" it if that is how the equation works.

As you can tell, I might need a bit of help with this one but I do appreciate it.

Steve

4. ## Re: Help With A Rocket & Its Velocity / Range

What course are you taking that assigned this problem? ... or are you just attempting it on your own?

5. ## Re: Help With A Rocket & Its Velocity / Range

No, I am not taking a course at all. It was just a math problem that has cropped up. Small part of a much larger puzzle. As I am not very good at Maths I thought I might get the answer / help on this forum. Hope this is OK.

6. ## Re: Help With A Rocket & Its Velocity / Range

I was not sure what forum to place this message in. I initially put it into the Trig forum but it got moved to this forum by an administrator. Hope to get and answer / some help.

7. ## Re: Help With A Rocket & Its Velocity / Range

This problem was correctly moved to this forum because it is a physics problem dealing with elementary projectile motion.

You've been provided the necessary formulas to compute the horizontal range. I recommend you access a scientific calculator and complete this small part of the larger "puzzle". I'm not going to provide you the solution.

8. ## Re: Help With A Rocket & Its Velocity / Range

No, I didn't expect a solution, just some help to find to find the solution myself. I thought my questions above were reasonable for someone with very little experience / knowledge in this field.
The formulas are fairly obvious but I am stumped with the "sin" and how to use it, with or without a scientific calculator (which I do have)
I only registered and posted on here as I thought someone might babysit me through the maths. Let me know if you can help me with my questions as above. If not I will need to try elsewhere and any pointers to a Math Help Site that could help would be appreciated.

9. ## Re: Help With A Rocket & Its Velocity / Range

Originally Posted by sjblencoe
No, I didn't expect a solution, just some help to find to find the solution myself. I thought my questions above were reasonable for someone with very little experience / knowledge in this field.
The formulas are fairly obvious but I am stumped with the "sin" and how to use it, with or without a scientific calculator (which I do have)
I only registered and posted on here as I thought someone might babysit me through the maths. Let me know if you can help me with my questions as above. If not I will need to try elsewhere and any pointers to a Math Help Site that could help would be appreciated.
I don't mean to be insulting but if you don't know how to use the sine, cosine, and tangent formulas then you have little chance understanding this material. I'd recommend studying some basic trigonometry before you attempt to do Physics.

There is very little we can help you with on this problem.

-Dan