Scenario 1: You work as a design engineer in SpaceX which is a space exploration company that produces re-usable space rockets. Space rockets in the past used to be disposable, the fact that they only serve for one time then get lost in the space. SpaceX proposed a re-usable rocket, that can go to outer space, deliver some equipment, satellites, or even people to the outer space, and get back to earth to land again in a specified parking point. Where it can be re-fuelled, go through careful maintenance, and go through another journey again. You are regularly requested by your manager to provide technical reports and theoretical explanations about the main components and operational concepts related to these space shuttles. [https://www.spacex.com/] Task 1: Concerned with the number of maintenance visits the rocket can undergo before being out of service, you have been informed that the recent statics show a that after the first journey to the outer space, the rocket was sent to service once, and after that the number of maintenance visits increase by 1 after every journey, for instance, after the second journey, the rocket had to go to service twice before being re-used, three-times after the 3rd use and so on. A. Generate a rule for the number of visits to the maintenance department with respect to space journeys, is this rule arithmetic or geometric. B. How many journeys will it take to for the number of service visits after a certain journey exceed 10? C. The rocket is not to be re-used again if the total number of maintenance visits exceed 50, then how many journeys will a single rocket serve before being out of service?

Question

Scenario 1:
You work as a design engineer in SpaceX which is a space exploration company that produces re-usable space rockets. Space rockets in the past used to be disposable, the fact that they only serve for one time then get lost in the space. SpaceX proposed a re-usable rocket, that can go to outer space, deliver some equipment, satellites, or even people to the outer space, and get back to earth to land again in a specified parking point. Where it can be re-fuelled, go through careful maintenance, and go through another journey again. You are regularly requested by your manager to provide technical reports and theoretical explanations about the main components and operational concepts related to these space shuttles. [https://www.spacex.com/]
Task 1:
Concerned with the number of maintenance visits the rocket can undergo before being out of service, you have been informed that the recent statics show a that after the first journey to the outer space, the rocket was sent to service once, and after that the number of maintenance visits increase by 1 after every journey, for instance, after the second journey, the rocket had to go to service twice before being re-used, three-times after the 3rd use and so on.
A. Generate a rule for the number of visits to the maintenance department with respect to space journeys, is this rule arithmetic or geometric.
B. How many journeys will it take to for the number of service visits after a certain journey exceed 10?
C. The rocket is not to be re-used again if the total number of maintenance visits exceed 50, then how
many journeys will a single rocket serve before being out of service?
While testing the path of the rocket while ascending towards the space, it was found that the rocket rises 480 Kilo-meters in the first minute and then rises 99% of the distance travelled in the previous minute for subsequent minutes.
D. Generate a rule for the distance travelled in each minute, is this rule geometric or arithmetic?
E. Find the maximum possible height that the rocket can reach.
F. If the cargo was a satellite, then it must be placed in the geostationary orbit [it is the orbit above earth
on which any placed object will remain fixed above a certain point on earth], which is 36’000 Kilo- meters above Earth’s surface. Determine the journey time required before switching the rocket engines off.
Through the design process, you need to check multiple details in various components and parts of the rocket systems. You had to solve the following equations throughout the process:
G. The voltage, V, across a capacitor is given by: V= 9(1 − ?−0.1?). Evaluate the time taken, t, for V to equal 3 volts, show all steps of your solution.
H. It is known that the total quantity within an exponential function[-0.1* t in the previous question]must be dimensionless. What is the dimension of the constant -0.1 in the previous equation?
I. In a thermodynamic system [like the rocket engine] we have the relationship
log(?) = ???? (?) + log(?)
where P represents pressure, V represents volume, C is a constant and n is an index. Show that:
??? = P
J. If in the previous question, n = 2, find the dimensions of the constant C.
K. The speed, v (m/s), of hot air coming out of the rocket engine is given by:
?2 = K? tanh(6.3?) ?
Where K is a constant and equals 36, d is the distance from the middle of the air stream in meteres, and λ is the wavelength in meters. Evaluate the speed v if d = 3.5 m and λ =30 m.
L. In the previous question, v is in m/s, d and λ are in meters, find the dimensions of the constant K.
M. You are designing a new engine; this device operates with liquid fuel as an input and generates energy as an output. During your experiments you found that the produced energy depends on the following: the density of the liquid, liquid pressure, and the initial power of the moving liquid being injected into the engine. Derive a formula that can be used to calculate the energy produced by the device in terms of the density, pressure and initial power of the moving liquid.
N. The figure below shows a trajectory of a satellite that is launched from point A using a rocket,to point C in space, this movement AC took a certain time. Then it moved towards point B [angle ACB is 90 degrees] in 1.455 hours. At this moment of time, the distance between the launching point and the satellite measured in travelling hours, AB = 1.9 hours. The angle ??? = 50.0°. Write down the vectors CB and AB in terms of i and j components [Cartesian format]. Write down an equation relating AC, AB and CB as vectors, then find the vertical travelling duration points A and C, or the vector AC? [Hint: you can simplify the problem by rotating the triangle such that AC coincides with the y-axis]

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