How Do You Calculate Rocket Trajectory and Impact?

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To calculate rocket trajectory and impact, the initial velocity for a vertically launched rocket is determined to be 24.99 m/s, achieving a maximum height of 31.8622 m before returning to the ground in 5.10 seconds. When launched at a 45-degree angle with the same initial velocity, further calculations are needed to determine the total time in the air, maximum height, and horizontal distance traveled. The discussion highlights the importance of understanding kinematic equations, as incorrect application can lead to errors in time calculations. A suggestion is made to consult physics textbooks for better comprehension of the concepts involved. Mastery of these principles is essential for accurate trajectory calculations.
Newell33
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Homework Statement



Use 4 decimal places at each step to ensure accuracy.
a) A rocket is launched vertically and remains in the air for 5.10 seconds until it hits the ground. Calculate the initial velocity of the rocket. Calculate the maximum height of the rocket (positive).
vo = 24.99

m/s (Note: You will need this initial velocity for parts b, c, and d)
y = 31.8622

m

b) The rocket is now launched with the same initial velocity as calculated in part A at an angle of 45 degrees. Calculate the time the rocket will be in the air for. Calculate the maximum height that the rocket will reach. Calculate the horizontal distance that the rocket will travel until it hits the ground.
t = s

y = m
x = m


Homework Equations


idk sorry :(

The Attempt at a Solution



ok so i tried to do
t = (v - vo) / -9.8


and its wrong because i got
2.55
 
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If you don't know the kinematic equations, you won't be able to do solve these questions unless you know how to derive them yourself. You can find some of the formulas (not all of them, but you can derive the rest from the basic ones) in the sticky for this forum: https://www.physicsforums.com/showthread.php?t=110015
 
Do you have a physics textbook? If yes which one is it? I think I got through intro physics by studying the worked examples in my physics book (and also reading the book).
 
This: t = (v - vo) / -9.8
gives you only half of the time because its speed is (momentarily) zero at the top.
Its speed is not zero when it hits the ground!
 
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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