Finding rocket altitude and launch angle from flight time and landing distance

[353535amelia]

Homework Statement

I have the time and distance measurements. We shot it straight up, how can I find the altitude and angles? Times: (6.58 sec, 23 m), (6.90 sec, .6 m) (6.20 sec, 10 m). The time represents how long it takes for the rocket to shoot up and fall, the distance is the measurement from where it shot up to where it landed. We also had to determine the velocity and the wind velocity so I already have that. (v=v0+at; v=vi+2at) Idk the exact equation for the altitude and angles?

Homework Equations

Altitude? Angles?

The Attempt at a Solution

I tried to get the altitude to be about 53 I used the equation 1/2g(time/2)^2 so for example 1/2*(9.8)*(6.58/2)^2 or 1/2*(9.8)*(3.29^2)=53.03809, but the teacher said it was wrong... :( The angles I have no clue.

 

[haruspex]

You list several times and distances but don't say what they represent.

 

[353535amelia]

You list several times and distances but don't say what they represent.

Sorry. I edited it some.

 

[haruspex]

You said you shot the rockets straight up. If so, the horizontal displacement should be only due to wind (and the launch angle to the vertical is always zero), but I would have thought it was rather tricky to be sure you were launching straight up.
Since the launch angle will surely vary some, and the wind will vary, and the fuel content etc. of the rockets will vary, it is not going to be possible to combine the results to come up with one set of answers. Moreover, you cannot separate launch angle from wind on anyone test, so I would say you have been given an unreasonable task.

One option is to assume the rockets were launched vertically, and that the variation in horizontal displacement and time aloft are due to wind and rocket fuelling. That will allow you to find the height reached, separately for each test. Since the horizontal displacement is assumed to be entirely due to wind, you may be able to estimate the wind speed too, but you to do that you might have to make some assumption about the drag coefficient ( it won't instantly start moving sideways at the wind speed).

Another option is the other extreme - assume there is no wind and that the variation in horizontal displacement is entirely due to launch angle. That should allow you to determine (separately for each test) the height reached and launch angle.