Having trouble finding trajectory of a small rocket

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The discussion revolves around calculating the trajectory of a small rocket using limited data collected during its launch. Key points include the need for formulas to determine the magnitude of thrust and gravity, average acceleration, and velocities during the rocket's flight phases. The user has calculated the height of the rocket at its apex as approximately 408.01 meters and derived a final velocity of about 85.003 m/s, leading to an average acceleration of 17.709 m/s². There is confusion regarding the relationship between thrust and gravity, as the calculated thrust appears to be less than the gravitational force acting on the rocket. The user seeks clarification on these calculations and the physics concepts involved.
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Homework Statement



So we launched small rockets on our last day, but have a week to turn in the homework based on the launch, but seeing as we aren't allowed back in school I can't ask questions I am lost. We haven't dealt with anything remotely related to trajectory since the beginning of fall. I'm confident in doing the math needed, I just need help remembering some formulas. some outstanding questions are-

* Magnitude of the 2 main forces acting on the rocket ( thrust and gravity)
* average acceleration
* final velocity
* initial velocity when rocket enters coasting phase


the only data we collected at the launch was the angle of the flight path and we timed the rockets path from ignition to the apex of flight. I have no idea how to get the velocity or acceleration from that.

if you want my numbers, M of rocket+engine = 37.6 grams, M of Engine = 19.1 grams, M of Rocket = 18.5 grams, flight time to apex = 4.8 Sec, Height angle was 69 degrees measured 200 meters from the launch position. that's all the data i have. THANK YOU!

Homework Equations


like I said, its been a while and all I am really looking for is the relevant equations I need to solve the problems. We use basic algebraic equations. i remember a=v/t, v=d/t and that's all i remember.


The Attempt at a Solution



(Tan68) * 200= h
h= 408.01 meters
v=d/t
v= 408.01/ 4.8
v=85.003 m/s
a=v/t
a= 85.003/ 4.8
a= 17.709 m/s/s

(Magnitude of thrust)
would that be 5.03 * 37.6 = 189.128 N
(magnitude of gravity)
would that be 9.8*37.6 = 368.48 N
if so, how would the rocket fly seeing as the magnitude of gravity is > than magnitude of thrust?
 
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This is the actual worksheet that i have to fill out if you want to take a look at that
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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