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Problem solving task 1 (PST-1)MZB125 Introductory Engineering Mathematics

Due 11:59pm Friday week 9 – weighting 20% [20 marks]Queensland University of Technology

Semester 1, 2018• You must submit your attempt at this task via the MZB125 Blackboard site under the Assessment

page submission link• You must submit one file only, and the file is to be in PDF format.• You must keep a copy of the assignment file you submit.• See the Unit Guide (pages 5 and 6) for important information on QUTs policy for assignment

extensions and late submissions.• To obtain full marks for each of the questions, you need to show detailed working.Available marks for each question and sub-components of questions are indicated.

11 Trajectory of a rocket [5 marks]Consider a rocket initially located at the origin: (0,0,0). This rocket is fitted with a simple transmitting device that relays information about the rocket’s movement. Each transmission contains a vector

describing the movement of the rocket, relative to the position of the rocket at the previous transmission.

The rocket returns the following transmissions in order (a then b then c). All transmissions are in

kilometres. We are not interested in what happens to the rocket after the third transmission:a =243 5

1035b = 2 411 30 7 3 5 c = 2 410 24 553 5(a) Suppose that at the time of the third transmission, the rocket is located at some point P. Determine

the vector, –! OP describing the position of the rocket relative to the origin, AND determine the distance

of the rocket from the origin [2 marks].

(b) Assume that the earth is flat, and that the rocket follows a straight trajectory between transmissions.

Calculate the pitch angle of the rocket (the angle the rocket makes with the xy-plane) at the time of the

third transmission [2 marks].

(c) Calculate the deflection of the rocket’s heading on the ground between the first and the third transmissions (i.e., the change in direction seen on the ground) [1 mark].

22 The Force (required to pull a cylindrical cage up a ledge)

Awakens [5 marks]Princess Leia designed a large cylindrical cage for detaining Jabba the Hutt. The cage is made of two

outer rings with a series of bars connecting these rings (think of a hamster wheel, but bigger). You need

to roll this cage to a desirable location, but as you are doing so you come across a ledge blocking your

path.

To roll the cage up the ledge; you decide that the best strategy is to tie a rope to the upper-most bar

(P) (which is directly above the centre (O) of the cage), stand on the ledge and pull. You pull with a

force F of magnitude F. The following figure outlines the scenario: </s…

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