REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE Two Dimensional Kinematics 1.2.0A-B Vectors Vectors must be added by arranging them head-to-tail A = 3 m at 20° B = 5 m at 160° AX = 2.82 m BX = -4.70 m AY = 1.03 m BY = 1.71 m RX = -1.88 m Ry = 2.74 m 1.2.0 Two Dimensional Motion - Constant Velocity in Both Dimensions o When objects move in more than one dimension at a time (i.e. north-west), the motion can be broken into two separate motions. o Trigonometry may be used to break the problem into two parts. Organize information into X/Y chart. Use information to solve one dimension – time is the ONLY variable that can be used to cross from one dimension to the other. Pythagorean Theorem can also be used to find the resultant of two motions. Example: 1. A hockey puck moves north with a speed of 6 meters per second. At the same time, the puck drifts west at a speed of 2 meters per second. In the amount of time that it takes the puck to slide 24 meters north, it will also drift 8 meters west. 1 REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE 2. The northward component of a boat’s velocity is 6 meters per second while the east ward component of its velocity is 9 meters per second. The boat’s resultant velocity is 10.8 meters per second. The boat will move with an angle that is 33.7° north of east. 1.2.1A-F Ground Launched Projectiles o Projectiles follow parabolic paths. o Break initial velocity into components (if not given). o Organize vertical and horizontal givens into a chart. o Make necessary assumptions ax = 0 (assume no air resistance) ay = -9.81 m/s2 vix = vi cos θ viy = vi sin θ vy = 0 (at the maximum height) time to top = ½ total time of flight o o o For greatest height and/or flight time a projectile should be fired at 90°. For greatest horizontal range a projectile should be fired at 45°. Projectiles fired with the same speed at complementary angles will have the same horizontal range. 2 REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE Example: 1. A projectile is fired with an initial velocity of 12 meters per second at an angle of 30°. Breaking the problem down we get… 1.2.1G-K Horizontally Launched Projectiles Organize vertical and horizontal givens into a chart. o Make necessary assumptions ax = 0 (assume no air resistance) ay = -9.81 m/s2 viy = 0 vix = initial velocity time is the same in both dimensions o Any two objects released from the same height will hit the ground at the same time regardless of starting horizontal velocity! 3 REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE Example: 1. A projectile is fired horizontally with an initial velocity of 10 meters per second from a height of 6 meters above the ground. Breaking the problem down we get… 2. A projectile is fired horizontally from a height of 2 meters above the ground and travels 14 meters horizontally before it lands. 3. A projectile is fired horizontally with a speed of 8 meters per second and travels 16 meters horizontally before it lands. 4