Question

Let us assume we have a payloadwe wish to launch as high in the air as we can, and by chance we have two identical rocket engines. Maximum altitude of the payload would certainly be a good measure of the rockets performance. What combination of engines and firing sequence will lift the payload the highest? 2nd Stage fires at peak altitiude 2nd Stage fires at burnout Rajah 1: Figure 1 Described below are two ways to use two serially-staged rocket engines: 1. Launch a payload-engine combination with one engine, and when the combination reaches its peak altitude, fire the second engine to shoot the payload further aloft. 2. Launch a payload-engine combination with one engine, as soon as it is spent (burnout) fire the second engine to give the payload additional velocity aloft Which method reaches the highest altitude? Justify your answer using your knowledge of mathematics, sciences, engineering fundamentals and/or engineering specialization. Hint: Use conservation of mechanical energy: eTVconstant and T2 and V mgH, where m, , and H are mass, velocity and altitude respectively

please answer ASAP

Answer 1

From given the above mentioned both types are serial stage or tandem stage operations.

In which the first stage and second stage are serially attached to one another to launch the rocket.

Initially boosters are used to lift the rocket which is also know as zero stage.

Later first stage is fired to reach up to required velocity later the second stage starts running but completion time is less than the first stage.

From given two conditions the first condition help the rockets payload to reach maximum altitude when compared to the second condition.

FOR FIRST CONDITION:

In this condition given that the multi stages are combined to one engine and the stages are detached when the rocket reaches the peak altitude.

This condition helps in reaching high altitude because in this the rocket has positive velocity during stage exchanging there is no loss in velocity in the rocket, which is a positive point in this condition.

Since there is no loss of velocity during the travelling the rocket can reach the high altitude.

FOR SECOND CONDITION:

In the second condition given that the rocket will have multi stage but the next stage will start only after the completion of the precious stage which is a draw back in this operation.

When we wait until the completion of the stage the during the time of next stage the rocket will run only using its momentum which results in loss of velocity. So to over come the loss some of the velocity is utilised that's why we can't reach the maximum altitude.

CONCLUSION :

From above two condition we conclude that if we prefer the first condition we can reach the maximum altitude compared to the second condition due to velocity losses.