How Do You Calculate Rocket Trajectory and Impact?

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SUMMARY

The discussion focuses on calculating rocket trajectory and impact using kinematic equations. The initial velocity of the rocket is established at 24.99 m/s, resulting in a maximum height of 31.8622 m when launched vertically for 5.10 seconds. For a launch angle of 45 degrees with the same initial velocity, participants are tasked with calculating the total time in the air, maximum height, and horizontal distance traveled. A key takeaway is the importance of understanding kinematic equations to solve these problems accurately.

PREREQUISITES
  • Kinematic equations for projectile motion
  • Understanding of vertical and horizontal motion components
  • Basic physics concepts such as velocity and acceleration due to gravity
  • Ability to perform calculations with significant figures
NEXT STEPS
  • Study the derivation of kinematic equations for projectile motion
  • Learn how to calculate the range of a projectile launched at an angle
  • Explore the effects of air resistance on projectile motion
  • Review physics textbooks for worked examples on projectile motion
USEFUL FOR

Students studying physics, educators teaching projectile motion, and anyone interested in the mathematical modeling of rocket trajectories.

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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