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Vectors & Projectiles Study Guide Projectile Review 1. What variable represents “total horizontal displacement”? dx 2. Refer to the diagram • What is the acceleration of the rock at the beginning right after it is thrown? At the bottom right before it lands? horizontally = 0m/s2 vertically = 9.8m/s2 3. What is the initial vertical velocity? 0 m/s 4. If the initial horizontal velocity is 45m/s, what is the horizontal velocity after 2 sec? 45 m/s What is the horizontal velocity as it hits the ground? 45m/s (Horizontally velocity remains constant and never changes) 5. What does range refer to? The horizontal displacement of the projectile 6. For an angled projectile - Which angle produces the maximum range? 45-degree 7. If the initial angle is 30 degrees, what other angle will give the same range? What are these angles called? What is the relationship between the angle of the projectile and time in the air? 60o , complementary angles Larger angle = more time in air So complementary angles have the same range, not the same height 8. Define a projectile: a form of motion in which an object moves along a curved path under the action of gravity only. 9. According to the definition of a projectile why are each of the following considered projectiles? a. a dropped rock b. a rock thrown horizontally c. a rock thrown vertically up d. a rock thrown at an angle In each case once the rock is released the only thing acting on it is gravity What does the word “trajectory” refer to? the path followed by a projectile Describe how perpendicular motions (2-D) (horizontal and vertical) affect each other. •They don’t – they are totally independent of each other. Which two things below does the angle of a launched projectile affect? Height Range 13. If you want to increase the amount of time it takes a horizontal projectile to land, Which of the following needs to increase? Height 14. If you want to increase the range of a horizontal projectile, which of the following needs to increase? Initial Velocity 15. A 5kg object and a 10kg object are both launched from the same cliff at the same time. How will the difference in mass affect each of the following? a. time to fall b. range c. acceleration d. final velocity mass has no effect on projectile motion 16. What is the vertical acceleration of: a horizontal projectile b. angle projectile c. dropped object 9.8m/s2 Use the diagram above to answer the following questions (#17-21): 17. If the Vx = 30m/s at point X what will it be at: a. point Z? b. point Y? c. Point P? It will be 30m/s at all points (Horizontal velocity is constant) 18. If the Vy = 15m/s at point X what will it be at: a. Point Y (0 m/s) b. Point Z (15m/s) 19. If it takes 2.8s for the projectile to rise from X to Y how long will it take for it to fall from Y to Z? 2.8s 20. What is the acceleration of the projectile at Point Y? at point P? 9.8m/s2 vertically 21. If the projectile above had been aimed straight up instead of at an angle at a velocity of 33m/s what would be the velocity of the object when it landed? 33m/s It loses all of its velocity going up but then gains it all back on its way down. Vector Review What is the difference between a scalar quantity and a vector quantity? Scalar: Magnitude only Vector: Magnitude and direction What is the symbol for a vector? • -a vector is represented by an arrow tipped line segment. 3. How is a resultant drawn on a vector diagram? from the tail of the first vector to the head of the last vector 4. What is a tailwind? wind that blows in the direction of travel of an object, increases objects velocity A headwind? headwind blows against the direction of travel, decreases objects velocity For the following quantities, determine which are vectors and which are scalars. Position (v) c. Speed (s) Length (s) d. Mass (s) Force (v) h. Velocity (v) Price (s) i. Time (s) Distance (s) j. Displacement (v) 6.What is the difference between total distance and total displacement? -Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. -Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. 7. What is the difference between a resultant vector and component vectors? -The resultant vector describes the whole vector, magnitude as well as direction -The component vector describes just one element of a vector, just like the xcomponent. Components Resultant 8. When solving vector problems, we draw our diagrams using the head-totail method. What does this mean? -the head of this first vector ends, the tail of the second vector begins If you are given 2 component vectors of varying direction, what will be the range of the resultant? Minimum = subtracting the 2 vectors Maximum = adding the 2 vectors. A stone is thrown horizontally at a speed of 20m/s from the top of a cliff 80m high. Horizontal Vertical Vx=20m/s dy=80m a. How long does it take the stone to reach the bottom of the cliff? b. How far from the base of the cliff does the stone land? Vector Problems – You must do the following for each vector problem on the test: • • • • • Draw a vector diagram to represent the problem. Label vectors. Solve the problems mathematically using the formula(s) provided. Show the formula(s) used. Show all work. All answers should be recorded as follows unless specified differently. Ex: 12km, 30 degrees, North of West Put answers in the blanks provided. Vector Problems – A runner traveled 15 km west then backtracked 11km east, then traveled 6km west before stopping. What is the runner’s total displacement? What is the total distance walked? Displacement = 10 km, West Distance = 32km 15 km west 11 km east 6 km west While flying due east at 120km/h, an airplane is also carried northward at 45km/h by the wind blowing due north. What is the plane’s resultant velocity? (Magnitude and direction) _____, _____, ___ of ___ 45 km/hr North Θ 120 km/hr East Pythagorean Theorem c2=452 +1202 c2=16425 c=√16425 c=128 km/hr Theta Opp/adj 45/120= 0.375 Tan-1 of 0.375 =20.55o 128 km/hr, 21o, North of East An airplane is flying 340 km/hr at 26 0 North of east, what would be the north and east components of the airplane? θ • You would draw the longest vector first (east), then the second vector • • • Remember theta is drawn at the tail of the 1st vector North vector (y-component) = sin(26) x 340 = 149.05 km/hr East vector (x-component) = cos(26) x 340= 305.59 km/hr A rocket is launched at an angle of 18 0 S of W with an acceleration of 118m/s2, what are the rocket’s vertical and horizontal accelerations? θ • You would draw the longest vector first (west), then the second vector • • • Remember theta is drawn at the tail of the 1st vector South vector (y-component) = sin(18) x 118 = 36.46 m/s2 West vector (x-component) = cos(18) x 118= 112.22 m/s2