# Model Rocket Launch: Maximum Height, Time, and Duration Calculations

• Zacharrry
In summary, a model rocket is launched with an initial speed of 50.0 m/s and accelerates with a constant upward acceleration of 1.50 m/s2 until its engines stop at an altitude of 110 m. To find the maximum height reached by the rocket, you need to consider the two parts of flight separately and find the time and speed at 110 m. Once you have this information, you can determine the time it takes for the rocket to reach its maximum height and the total time the rocket is in the air. A diagram can be helpful in setting up the problem and identifying what information is needed at each point in the flight.
Zacharrry

## Homework Statement

A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 1.50 m/s2 until its engines stop at an altitude of 110 m.
(a) What is the maximum height reached by the rocket?
(b) How long after lift-off does the rocket reach its maximum height?
(c) How long is the rocket in the air?

## Homework Equations

One of the "big four" kinematics equations.

## The Attempt at a Solution

I am having difficult setting the problem up and finding an answer for each of the questions.

Consider the two parts of flight separately.

For the first part you need to find the time and the speed at 110 m

When you have that speed, you can tackle the second part of the flight and find that time.

I would sketch a diagram and mark in what you know and what you need to know at the specified points - ground, 110 m and top.

## 1. How do you calculate the maximum height of a model rocket launch?

The maximum height of a model rocket launch can be calculated using the formula h = v02sin2(θ)/2g, where h is the maximum height, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s2).

## 2. What factors affect the maximum height of a model rocket launch?

The maximum height of a model rocket launch is affected by the initial velocity, launch angle, air resistance, and the weight of the rocket. Higher initial velocity and smaller launch angles will result in a higher maximum height, while air resistance and a heavier rocket will decrease the maximum height.

## 3. How do you calculate the time of flight for a model rocket launch?

The time of flight for a model rocket launch can be calculated using the formula t = 2v0sin(θ)/g, where t is the time of flight, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s2).

## 4. Can you calculate the duration of a model rocket launch?

Yes, the duration of a model rocket launch can be calculated by subtracting the time it takes for the rocket to reach its maximum height from the total time of flight. This can be calculated using the formula td = t - (2v0sin(θ)/g), where td is the duration of the launch, t is the total time of flight, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s2).

## 5. What is the importance of calculating maximum height, time, and duration for a model rocket launch?

Calculating the maximum height, time, and duration of a model rocket launch allows for a better understanding of the performance of the rocket. It also allows for comparisons between different launches and can help in making adjustments to improve future launches. Additionally, these calculations can help in predicting the landing location of the rocket.

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