MCV4U Assignment - Applications of Vectors Name: Answer the following questions by showing your work, using proper mathematical terminology and format, including labeled diagrams, and writing conclusions. Round to two decimal places. Part of being a mathematician is solving problems efficiently; to earn full marks, solutions need to be correct and efficient (See the back of this page for a rubric for the Thinking and Communication categories). Write your good copy on separate paper. 1. Youssef, Shehab, and Mohy are moving some heavy speakers for a school event. To make it easier, they put the speakers on a trolley with wheels (the kind that spin to allow the trolley to go /8 in any direction, not just backwards and forwards) and attach three ropes to the front. Youssef pulls straight ahead with a force of 80 N; Shehab pulls at a 24" angle to Youssef's left, and Mohy pulls at a 30" angle to Youssef's right. If Shehab pulls with a force of 60 N, at what force would Mohy have to pull in order for the cart to go straight (in Youssef's direction)? 2. Four forces are working against each other (on the same plane, so you don't need to consider three dimensional space). Two of the forces, of magnitudes 70 N and 50 N, act in opposite /7 directions to each other. The other two forces, of magnitudes 20 N and 60 N, act in opposite directions to each other as well. The 20 N force is at an angle of 40" to the 50 / force. Find the resultant force and the equilibrant force. 60 N 71 (50 N 20 N 70 N 3. Is it possible for three forces of 19 N, 14 N, and 35 N to keep a system in a state of equilibrium? If it is possible, draw a vector diagram, labeling sides and angles. If it is not possible, explain why, /4 providing mathematical evidence to support your claim. 4. A mass of 50 kg is supported from a ceiling by two ropes of length 30 cm and 20 cm. The ropes are attached to the ceiling 45 cm apart. Determine the tension in each of the ropes. /11