# Finding max height for a rocket with upwards acceleration

• garcia1
In summary, the toy rocket will achieve the maximum height it can achieve if the acceleration of gravity is 9.8 m/s2.
garcia1

## Homework Statement

A toy rocket, launched from the ground, rises
vertically with an acceleration of 23 m/s2 for
11 s until its motor stops.
Disregarding any air resistance, what max-
imum height above the ground will the rocket
achieve? The acceleration of gravity is
9.8 m/s2 .

## Homework Equations

I used kinematics equation: x=Vo*t + 1/2at^2

## The Attempt at a Solution

I was a little unsure how to go about this problem, since most free fall problems I've dealt with use only gravity as acceleration.

I tried plugging the following values into my equation:
Vo = 0m/s
a = 23 m/s^2
t = 11s

I got the answer 1391.5m, but this was wrong. I think the problem is simpler than I'm thinking about it, but I can really use some help on this.

hi garcia1!

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garcia1 said:
I tried plugging the following values into my equation:
Vo = 0m/s
a = 23 m/s^2
t = 11s

I got the answer 1391.5m …

that's the height at the end of the first stage …

you still need the extra height that it goes with a = -9.81 m/s2

So what I did next is solve for the final velocity of part 1 by using the fact that Vo = 0m/s since the rocket starts from rest. Using the equation V = Vo + at, I got the equation

V = 23*11 = 253m/s

With this I placed this final velocity as the initial velocity for the next segment. I determined in this 2nd segment that X = ?, Vo = 253m/s, a = -9.81m/s^2, and Vf = 0, since the rocket must come to rest at the final height before falling.

I got the following equation:
Vf^2 = Vo^2 + 2ax -> x = Vf^2 - Vo^2 / 2a.

This answer was 3265.76m. Adding this to the initial 1391.5m, I got 4657.27m. This was wrong though, so I think there is something in this second step I'm getting wrong. Any thoughts?

Did you answer in terms of km, or in terms of m?

Last edited by a moderator:

## 1. How do you calculate the maximum height of a rocket with upwards acceleration?

The maximum height of a rocket can be calculated using the equation h = (v02sin2θ)/2g, where h is the maximum height, v0 is the initial velocity, θ is the angle of elevation, and g is the acceleration due to gravity.

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

The maximum height of a rocket is affected by the initial velocity, angle of elevation, and the acceleration due to gravity. Other factors such as air resistance, wind, and weight of the rocket can also impact the maximum height.

## 3. How can you increase the maximum height of a rocket?

The maximum height of a rocket can be increased by increasing the initial velocity or the angle of elevation. Reducing air resistance and using lightweight materials can also help increase the maximum height.

## 4. Can the maximum height of a rocket ever be infinite?

No, the maximum height of a rocket is limited by factors such as air resistance and gravity. It cannot continue to accelerate upwards indefinitely.

## 5. Why is it important to calculate the maximum height of a rocket?

Calculating the maximum height of a rocket is important for understanding its performance and capabilities. It can also help in designing more efficient and successful rockets for future launches.

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