Calculating Total Flight Time for a Rocket: A Scientific Approach

In summary, the conversation discusses the calculation of various parameters related to a rocket's flight, including the velocity before ground impact, at the end of engine burn time, and at maximum altitude, as well as the total flight time. The conversation also mentions a potential error in the calculation and the need to determine the velocity at maximum altitude.
  • #1
ColeridgianHam
1
0
Homework Statement
A missile silo is used to launch interplanetary rockets vertically upward out of the silo, giving the rocket an initial speed of 80.2 m/s at ground level. As the rocket clears the silo, the engines fire, and the rocket accelerates upward at 3.80 m/s^2 until it reaches an altitude of 1,080 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s^2.
Determine the rocket's velocity (in m/s) just before ground impact and its total time of flight (in s).
Relevant Equations
t=(Vx-Vi)/a
I calculated the time for the velocity before ground impact, which is v = -189.23 and the velocity at end of engine burn time, which is 120.996. I also calculated the max altitude (y = 1826.94), and the time to reach the max altitude was t = 23.0823 seconds. So from this information, I did:
t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.
Since the question asked for total flight time, I added this time together with the time to reach the maximum altitude:
6.9626s + 23.0823s = 30.0449 seconds
However, I was told my calculation for the total flight time is wrong, while everything else is correct. Where did I mess up?
 
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  • #2
The rocket has initial velocity 80.2 m/s at groud level when t=0 s and go up to 1080 m with acceleration 3.80 m/s^2. When , say t1, the rocket reached hight 1,080 m ?. How much speed, say v1, does it have then?

The rocket free falls with initial velocity v1 with gravity g downward at t=t1 second. When, say t2, the rocket crash to ground ? How much speed, say v2, does it have then?
 
  • #3
ColeridgianHam said:
t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.
Since the question asked for total flight time, I added this time together with the time to reach the maximum altitude:
But t is not the time to fall from max altitude. What is the velocity at max altitude?
 
  • #4
ColeridgianHam said:
t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.
This figure is supposed to have been the time taken for the Earth's gravity to reverse a 120.996 meter per second upward velocity into a -189.23 meter per second downward velocity.

Can you see a sign error in the calculation?
 
  • #5
mjc123 said:
But t is not the time to fall from max altitude. What is the velocity at max altitude?
Your point is valid, but having corrected the calculation of that t (per post #4) it would be simpler to consider what time should be added to it to get the total flight time.
 

FAQ: Calculating Total Flight Time for a Rocket: A Scientific Approach

1. What is the definition of total flight time of a rocket?

The total flight time of a rocket refers to the duration of the entire flight, from the moment of launch until the rocket reaches its final destination or falls back to Earth. It includes the time spent in the atmosphere and in space.

2. How is the total flight time of a rocket calculated?

The total flight time of a rocket is calculated by adding the time it takes for the rocket to reach its final destination or return to Earth, known as the time of flight, to the time it takes for the rocket to accelerate and decelerate, known as the time of acceleration and deceleration.

3. What factors affect the total flight time of a rocket?

The total flight time of a rocket can be affected by various factors such as the distance of the destination, the speed and acceleration of the rocket, the efficiency of the rocket's propulsion system, and any external forces such as gravity and air resistance.

4. Can the total flight time of a rocket be shortened?

Yes, the total flight time of a rocket can be shortened by increasing its speed and acceleration, reducing the distance to the destination, and improving the efficiency of its propulsion system. However, these changes may also require more fuel and resources.

5. Is the total flight time of a rocket the same for all rockets?

No, the total flight time of a rocket can vary depending on its design, purpose, and destination. Rockets with different propulsion systems, payloads, and destinations will have different total flight times.

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