Calculating Maximum Height and Flight Time of a Model Rocket Launch

In summary, the model rocket was launched with an initial speed of 54.4 m/s and accelerated at a constant rate of 2.20 m/s2 until its engines stopped at an altitude of 131 m. To find the maximum height reached, we use the equation Vf^2=Vi^2+2ad and solve for d, which gives us a value of 673 m. However, after the engines stop, the rocket is in free fall with an acceleration of -9.8 m/s2. Using the same equation with a different acceleration, we can find the height reached during this second part of the motion, which is 445.08 m. Therefore, the maximum height reached by the rocket is
  • #1
gadawg90
18
0
A model rocket is launched straight upward with an initial speed of 54.4 m/s. It accelerates with a constant upward acceleration of 2.20 m/s2 until its engines stop at an altitude of 131 m. What is the maximum height reached by the rocket? How long after lift off does the rocket reach its maximum height? How long is the rocket in the air?

well i was thinking that the velocity final would be 0 since at the top it would stop for a very short time, so i plugged the numbers into the equation
Vf^2=Vi^2+2ad and solved for d, but that's not right.i got 673 m
 
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  • #2
You need to do this in two parts. Don't forget that the rocket doesn't come to a dead stop once its engines stop running. The equation that you quoted can give you the speed of the rocket until its engines stop at an altitude of 131 m. Finding that speed is the first part. After that the rocket is in free fall, but climbs even higher. How much higher? That's the second part.
 
  • #3
alright well i found the velocity final at 131 m to be 93.40 meters, so would i use the same equation and use that as my velocity initial and my velocity final be 0?
 
  • #4
Yes, the same equation, but with different acceleration, of course.
 
  • #5
sorry, but would it turn into a free fall question and the acceleration be -9.8? i tried it and it was wrong..
 
  • #6
gadawg90 said:
sorry, but would it turn into a free fall question and the acceleration be -9.8? i tried it and it was wrong..

Yes, it turns into a freefall question. Can you post your solution? It shouldn't be wrong.
 
  • #7
Alright so i set up the second equation like this
0=93.4^2 + 2(-9.8)d
and for d i got 445.08 m
 
  • #8
That looks about right. So what is the maximum height reached by the rocket?
 

1. What is the maximum height an object can reach?

The maximum height an object can reach is dependent on several factors, such as the initial velocity and angle of launch, air resistance, and gravity. In a vacuum, the maximum height would be infinite, but in real-world scenarios, it is limited by these factors.

2. How is the maximum height of an object calculated?

The maximum height of an object can be calculated using the equation h = (v2sin2θ)/2g, where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This equation assumes no air resistance and a constant gravitational force.

3. Is the maximum height of an object affected by its mass?

Yes, the maximum height of an object is affected by its mass. In the absence of air resistance, objects with different masses will reach the same maximum height if they are launched with the same initial velocity and angle. However, in real-world scenarios with air resistance, mass does play a role in determining the maximum height an object can reach.

4. Can the maximum height of an object be greater than its initial height?

Yes, the maximum height of an object can be greater than its initial height if it is launched at an angle greater than 90 degrees. In this case, the object will reach its maximum height at the highest point of its trajectory before falling back down.

5. What is the difference between maximum height and maximum altitude?

The maximum height of an object refers to the highest point it reaches vertically. On the other hand, maximum altitude is the highest point an object reaches in relation to the surface of the Earth. Maximum altitude takes into account the curvature of the Earth and is often used in aviation and space travel.

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