2013 sample vector kin dyn test.notebook September 20, 2013 1) Draw a vector diagram illustrating how to add displacement vectors of 45 m [E] and 45 m [30o S of E], then solve the problem algebraically. (3 marks) Rx = 45 [E] + 45 cos 30 [E] = 84 m Ry = 45 sin 30 [S] = 22.5 30 o |R| = √ (842 + 22.52) = 87m at an angle of tan1(22.5/84) = 87 m [15o S of E] 2) If a plane flew NW for 320 km then changed course and flew another distance and ended up 250 km due West of its starting point, what was the distance and direction of the course change? (3 marks) Ay = 320 sin 45o = By =226 km A B 45o R Ax + Bx = 250 Ax = 320 cos 45o =226 km Bx = 250 226 = 24 |B| = √ (Bx2+By2) = 228 [84o S of W] or [6o WofS] 1 2013 sample vector kin dyn test.notebook September 20, 2013 A car travelling at 60.0 km/h applies the brakes and decelerates at one gforce 9.8 m/s2 . What is the time and distance needed for it to come to a complete stop? What is the distance needed for the same car going only 30.0 km/h to come to a complete stop? (4 marks) 60 km/h = 16.666 m/s t= (vf vi ) / a = 16.666/9.8 = 1.70 s d= (vf 2 vi 2) / 2a = 14.17... m or d=vt where v is average of 16.66 and 0 , 8.33*1.7 = 14.17... For 30.0 km/h = 8.333 m/s, same calc. gives 3.54 m ( 1/4 of previous) A catapult shooting at an angle of 12o from the horizontal fires a rock at 35 m/s. What is the range of the catapult at this angle? What will the height of the rock be when it has travelled only 11 m forward? (4 marks) dx = vx * ttotal ttotal= 2 ( vyi / 9.8) vx= 35 cos 12 = 34.2... vy= 35 sin 12 = 7.2... dx = 50.8 m When dx = 11, t = 11/34.2... = 0.321...s dy = vyit + 0.5 at2 = 7.2..*.321.. 4.9 (.3212) = 1.83m A boat crossing a river is capable of a 7.0 m/s speed relative to the water, and the river flows to the North at a rate of 2.4 m/s. If the river is 128 m wide, and the boat is aimed straight across, how long does it take to reach the other side, and how far upstream or downstream will it move relative to its starting point? (4 marks) 2 2013 sample vector kin dyn test.notebook September 20, 2013 A 75.5 N force is applied to slide a 10.2 kg block horizontally, and its acceleration is 5.5 m/s2 to the left. What is the force of friction on the block, and in what direction? (2 marks) A sign weighing 450 N is suspended from a rope that is tied to two other ropes which are tied to the ceiling. The left rope makes an angle of 35o to the ceiling, the right one is at 47o to the ceiling? What is the tension in each of the three ropes? (4 marks) A 9.0 kg mass is on a ramp angled 25o from horizontal. If it slides down the ramp with an acceleration of only 2.7 m/s2 what is the force of friction and coefficient of friction ? (4 marks) 4) An Atwood machine has a 4.5 kg mass and a 6.0 kg mass attached over a frictionless pulley . What is the acceleration of the 6.0 kg mass, and the tension in the rope? (2 marks) 3 2013 sample vector kin dyn test.notebook September 20, 2013 4