MATH1050/7050Semester 2, 2020Assignment 1All questions must be submitted by4 pm on Friday 21 August. Prepare your assignment as a single pdffile, either by typing it or by scanning your handwritten work. Upload your submission using the assignmentsubmission link in Blackboard. Your submission must adhere to the presentation and legibility guidelinesoutlined on Blackboard.Remember that your assignment must be your own work. You shouldshow all working.1.A particle with position vectorr= 5i−3j−k(m) has a forcef=−2i+j+ 9k(N) acting on it. Determinethe magnitude (to 1 decimal place) of the torque about the origin.(3 marks)2.Three pulling forcesF1,F2andF3are acting on a particle,p, as indicated in the diagram below (notto scale) whereθ1= 45◦andθ2=θ3= 30◦. If||F1||= 10 and the particle is at rest, determine themagnitude of vectorsF2andF3to two decimal places.(3 marks)pF1F2F3θ1θ2θ33.Find the point of intersection and the acute angle (in degrees and radians, to 1 decimal place) betweenthe lines described by the vector equationsr1=4−213+t1120andr2=2216+s125014.(4 marks)continued next page…1
4.A plane is flying at a constant altitude on a heading of N52◦E with a speed of 740 km h−1. Wind isblowing from the South East at a 37 km h−1.a) Find the magnitude of the resultant velocity of the plane to the nearest integer.(3 marks)b) How many degrees off course does the plane end up because of the wind? Give your answer to 2decimal places.(3 marks)5.a) Show thatzw=zw.b) Considerz= 4 + 2iandw= 7−i. Determine|(z+w)(z−w)|.(4 marks)6.Find the exact value of cis(π12)in the forma+biwherea,b∈R. Hence, use this result to determinethe exact value of tan(π12).(6 marks)7.Please copy the following declaration and sign your name below it to indicate your agreement:”I certify that my submitted answers are entirely my own work and that I have neither given nor receivedany unauthorized assistance on this assessment item.”2
