Projectile Motion: Homework Help for Max Height & Time in Air

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A model rocket accelerates at 5 m/s² for 10 seconds before its fuel burns out, and air resistance is ignored. To find the maximum height and total time in the air, the motion should be analyzed in two phases: the powered ascent and the free fall. After 10 seconds of acceleration, the rocket reaches a certain velocity and height, after which it will continue to ascend briefly before descending. The discussion clarifies that the fuel duration refers only to the initial 10 seconds of flight, not the total time until the rocket hits the ground. Understanding these phases is crucial for solving the problem effectively.
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Homework Statement


A model rocket has an acc of 5m/s/s while its fuel is buring. Its fuel lasts for 10 sec. ignore the air resistance.

Homework Equations


a) max height above the ground of this rocket?
b) the time this rocket in the air before it hits the ground?

The Attempt at a Solution


I have no idea about this question, and I'm going to cry because it's due on tomorrow... Please help me~[/B]
 
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You need to show an attempt. What equation will work for this question?
 
Here are the equations I try to use:
Vx =Vo+a*t
displacement x = t/2(Vo+V) = Vo*t+(1/2)*a*t^2
(Vx)^2 = (Vo)^2 + 2a*displacement
 
Those formulas are all you need. Split the motion into two parts - the time where the fuel is burning and the free fall afterwards.
What are velocity and displacement after 10 seconds? What happens afterwards?

You can assume that the rocket starts on the ground, at rest, and accelerates perfectly vertical. A good problem statement would have made this clear, but whatever.
 
mfb said:
Those formulas are all you need. Split the motion into two parts - the time where the fuel is burning and the free fall afterwards.
What are velocity and displacement after 10 seconds? What happens afterwards?

You can assume that the rocket starts on the ground, at rest, and accelerates perfectly vertical. A good problem statement would have made this clear, but whatever.
I'm not really understand this sentence from question, "Its fuel lasts for 10 sec" does it mean the time from the rocket start flying to hitting the ground. Or, other meanings...
 
HTT said:
I'm not really understand this sentence from question, "Its fuel lasts for 10 sec" does it mean the time from the rocket start flying to hitting the ground. Or, other meanings...

Assume at t = 0, the rocket is on the ground, and the fuel is ignited. The rocket takes off and flies straight up. At t = 10 s, the fuel is exhausted and the rocket is no longer accelerating due to the burning of the fuel. What happens next?
 
SteamKing said:
Assume at t = 0, the rocket is on the ground, and the fuel is ignited. The rocket takes off and flies straight up. At t = 10 s, the fuel is exhausted and the rocket is no longer accelerating due to the burning of the fuel. What happens next?
Thank you so much, I think I got it~.
 
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