MAST10005 Calculus 1 Semester 1, 2014 Assignment 5 cover sheet Student name: Student number: Tutor name: Tutorial time and day: Marking table*: Marking categories: Method (M) Question ? /3 Answer (A) /2 Reasoning (R) /2 Literacy (L) /1 Marking criteria Demonstrating a valid method required for the problem. Correct calculations, manipulations, and final answer. Clear and correct justification and explanation. Clear structure, and correct use of all mathematical notation. TOTAL: /8 *Note: This assignment will be partially marked: your tutor will be instructed to only mark certain questions for credit. The remainder will be left as self-assessment: you should check your answers using the solutions that will be uploaded to the LMS after the assignment is due. MAST10005 Calculus 1 Semester 1, 2014 Assignment 5 Due: 2pm, Monday 14 April. Late assignments will not be accepted. 1. Consider the ellipse given by the equation (x − 1)2 (y + 2)2 + = 1. 9 25 (a) Sketch this ellipse in the x-y plane. (You do not need to label intercepts, but other important features should be labelled.) (b) Particle A starts at the rightmost point of the ellipse and performs a circuit in the anticlockwise direction every 2π seconds. Give a set of parametric equations describing the xand y-coordinates of A as a function of time t. (c) Do the same for particle B, which starts at the leftmost point on the ellipse and performs a circuit in the clockwise direction every π seconds. Explain the differences between this and your answer to (b). 2. Bames’ brother Bamie is playing in an AFL game.1 He kicks the ball from position O = (0, 0, 0) towards the goal. The bases of the goalposts are at (40, 10, 0) and (40, 16.4, 0). The ball follows √ a path described by the parametric equations (x(t), y(t), z(t)) = (10t, 3t, 8 5t − 4t2 ) (where t is in seconds), until it hits the ground, at which point we will assume for simplicity that it stops and does not bounce. (a) At what time does the ball hit the ground? (b) If the ball passes between the goalposts, what must its x-coordinate be at that moment? What conditions must the time t and y-coordinate satisfy? (c) In the absence of any opposing players who might have been able to stop the ball, did Bamie score a goal? (d) Sketch a graph of the path the ball followed, as seen from above, i.e. in the x-y plane. Indicate the positions of the goalposts, and label the important features of the graph. Assignment Instructions This assignment is worth a compulsory 2% of your final MAST10005 mark. Submit your assignment to your tutor’s MAST10005 assignment box, near the north entrance of the Richard Berry building. You should present your work neatly on A4-sized paper, with your name and student number on each page, and include this cover sheet at the front. Full working must be shown in your solutions. Marks will be deducted for incomplete working, poor mathematical expression, and incorrect mathematical notation. Full solutions will be uploaded to the LMS after the assignment is due. 1 Not to be confused with Jamie Bond, who played in 1991, Round 17, Fitzroy vs. Melbourne.