Calculus and Vectors MCV4U Graded Assignment 3 Part 5: Application: (5marks each) /15 (Choose any 3) 1. A small airplane is flying due north at 150 km/h when it encounters a wind of 80 km/h from the east. What is the resultant ground velocity of the airplane? 2. A force f1 of magnitude 6 N acts on particle P. A second force, f2 , of magnitude 8 N acts at 60 to f1 . Determine the resultant and equilibrant of and equilibrant of f1 and f2 . 3. A 10 N force is applied at the end of a wrench that is 14 cm long. The force makes an angle of with the wrench. Determine the magnitude of the torque of this force about the other end of the wrench. 4. A child, sitting in the backseat of a car travelling at 20 m/s throws a ball at 2 m/s to her brother who is sitting in the front seat. a. What is the velocity of the ball relative to the children? b. What is the velocity of the ball relative to the road? 5. Kayla wishes to swim from one side of a river, which has a current speed of 2 km h, to a point on the other side directly opposite from her starting point. She can swim at a speed of 3 km h in still water. a. At what angle to the bank should Kayla swim if she wishes to swim directly across? b. If the river has a width of 300 m, how long will it take for her to cross the river? c. If Kayla's speed and the river's speed had been reversed, explain why it would not have been possible for her to swim across the river