How can I calculate the maximum height reached by a model rocket?

In summary, the conversation is about a question regarding the maximum height reached by a model rocket, which took 5.0 seconds to return to the launch site. The answer is approximately 120 m, but there is confusion about how to calculate it. One person suggests using the formula D=RT, while another explains that this only works when the acceleration is constant. They provide alternative methods using the formulas s(t) = 1/2 a t^2 and (-g/2)t^2, which calculate the distance fallen by the rocket in 5 seconds. It is also mentioned that if the acceleration is not constant, calculus would be needed to solve the problem.
  • #1
hlcfairy
I have to take a final soon and I have practise questions The only one here I am having trouble with is thislast one. This question bugs me and the answer key doesn't show how to do it

After a model rocket reached its maximum height, it then too 5.0 seconds to return to the launch site. What is the approximate maximum height reachd by the rocket? {Neglect air resistance.}

the answer is 120 m

the only info u have is time and acceleration

How do I go about doing it?
 
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  • #2
the rocket going up is confusing, but i think this is what you're looking for:
simply, D=RT (distance=rate x time, if you're not familiar with it)

my guess is that this is not correct becuase you have to take into account the return of the rocket because of gravity. so something you muliply by either 2 or 1/2. maybe...
 
Last edited:
  • #3
The question asks: how far does something fall in 5 seconds, when its acceleration (due to gravity) is a = 9.8 m/s^2?

s(t) = 1/2 a t2, where t = 5, yields 122.5 m.

- Warren
 
  • #4
Maximus, "D= RT" only applies when R is a constant.

If R is changing at a constant rate (that is the rate of change of R is a constant) then you can use an "averaging" method. When the rocket was at it's peak, it's speed was 0 (that's why it stopped going up!). After 5 seconds at a constant acceleration of -9.8 m/s^2, it's speed is -9.8*5= -49 m/s (Since the rate of change of speed, acceleration, is constant, you CAN use "RT"). The average of the two values is (0+(-49)/2= -24.5. Using that average value, in 5 seconds, the rocket will fall -24.5*5= -122.5 m. The rocket must have fallen from a height of 122.5 m, value chroot (Warren) gave.

Using "g" instead of -9.8 m/s^2 and t instead of 5 seconds, the two speeds are 0 and -gt so the "average" speed is (0-gt)/2= -gt/2.
Multiplying that by t to get distance gives (-g/2)t^2, the formula chroot used.

Again, this only works when the acceleration is constant (a very important special case!). If the acceleration (in general "rate of change of the rate of change") is not constant, then you will have to learn calculus!
 

What factors affect a rocket's maximum height?

The maximum height a rocket can reach is determined by several factors, including the size and power of the rocket's engines, the weight of the rocket and its payload, the angle of launch, and the atmospheric conditions such as air resistance and wind.

How is a rocket's maximum height calculated?

The maximum height a rocket can reach is calculated using the rocket equation, which takes into account the rocket's mass, the mass of its propellant, and the exhaust velocity of the propellant.

What is the record for the highest rocket launch?

The highest rocket launch recorded was achieved by NASA's Saturn V rocket, which reached a maximum height of 363,000 feet (110,582 meters) during the Apollo 17 mission in 1972.

Can a rocket's maximum height be increased?

Yes, a rocket's maximum height can be increased by using more powerful engines, reducing the weight of the rocket, and optimizing the trajectory of the launch. However, there are limitations due to factors such as Earth's gravity and the amount of propellant that can be carried.

Why is the maximum height of a rocket important?

The maximum height of a rocket is important because it determines the range of potential applications for the rocket, such as launching satellites into orbit or sending astronauts to the moon. It also reflects the capabilities and advancements in rocket technology and engineering.

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