Projectile Motion Vocabulary

Transcription

1 Projectile Motion Vocabulary Term Displacement vector Definition Projectile trajectory range 1 Page

2 What is a displacement vector? Displacement Vector of (10 m, 45 o ) 10 m θ = 45 o When you throw a ball it follows a curved path. The position of the ball is described by its displacement vector. Vector Addition Larry walks 10 meters West and 20 meters North. Use Pythagorean s theorem to determine Larry s displacement. Pythagorean Theorem Given Formula Solution a = 20 m a 2 +b 2 =c =c 2 b = 10 m = c = c 2 c = m 2 Page

3 Projectile Motion What is a projectile? Regardless of its path, a projectile will always follow these rules: 1. The path a projectile follows is called its. 2. The trajectory of a projectile is a. 3. The horizontal and vertical motions of a projectile are completely of one another. a. In the absence of air resistance, there is no net horizontal force on the projectile; therefore the projectile travels with a constant horizontal velocity. In the picture below the horizontal velocity is constant: 5 m/s. Notice how the vertical velocity changes. 3 Page

4 4 Page

5 b. In the absence of air resistance, gravity is the only vertical force on the projectile; therefore the projectile travels with a uniformly accelerated vertical motion. Every second, the vertical velocity of the projectile changes by 9.8 m/s (10 m/s) 4. Horizontal and vertical motion are completely of each other. Therefore, the velocity of a projectile can be separated into horizontal (v x ) and vertical components (v y ). v x = velocity in the x-direction v y = velocity in the y-direction 5 Page

6 5. For a projectile beginning and ending at the same height, the time it takes to rise to its highest point equals the time it takes to fall from the highest point back to the original position. 6. For a projectile beginning and ending at the same height, the initial speed is equal to its final speed. 6 Page

7 Projectile Motion What is a displacement vector? (p. 134) What is a projectile? (p. 137) What is trajectory and what type of shape does a projectile follow? (p. 137) What is range? (p. 137) What does it mean that the horizontal and vertical components of a projectile s velocity are completely independent of one another? Note the horizontal velocity of the ball in the picture below. Why doesn t it change? Why does the vertical velocity change? 7 Page

8 At the instant a horizontally held rifle is fired over level ground, a bullet held at the side of the rifle is released and drops to the ground. Ignoring air resistance, which bullet strikes the ground first? What is the equation to calculate the vertical velocity of a projectile? (p. 138) What is the equation to calculate the horizontal distance a projectile travels? (p.139) What is the equation to calculate the vertical distance a projectile travels? (p. 139) Complete the table below calculating the horizontal and vertical positions of a ball rolling off a cliff at 20 meters per second: (use data table on p. 139) Time (sec) Horizontal Position (m) Vertical drop (m) 8 Page

9 Range of a Projectile List two factors that affect how far a projectile will travel are: (p. 140) Which angle below produces the furthest range? (p. 140) What combination of angles produce the same range? Is there a pattern? (p. 140) Check Questions 1. What is the word for the horizontal distance a projectile travels? 2. What launch angle gives a projectile its greatest range? 3. Why does a projectile move in a curved path? 4. A ball kicked off the ground at an angle of 20 degrees and a ball kicked at an angle of degrees have the same range. 9 Page

10 Horizontal and Vertical Velocities A projectiles horizontal velocity is constant. A projectiles vertical velocity changes 9.8 m/s. v y = gt v y = vertical velocity g = 10 m/s 2 t = time Vertical Velocity Practice Problems 3. Chris drops a water balloon off the top of the school. What is the balloons vertical velocity if it strikes the ground 5 seconds later? 4. A package falls off an airplane. How fast is the package traveling if it is in the air for 12 seconds? 5. A skydiver jumps out of a plane. How fast is he traveling 8 seconds later right before he pulls his parachute? 10 Page

11 Horizontal and Vertical Distance d x = v x t d x = horizontal distance v x = horizontal velocity t = time d y = 4.9*t 2 d y = vertical distance t = time 1. While chasing the Road Runner, Wile E. Coyote makes wrong turn and ends up sliding horizontally off the edge of a high cliff. He leaves the edge of the cliff while traveling 35 m/s. He hits the bottom 4 seconds later. a. Find the horizontal distance the coyote travels. Given Formula Solution v x = 35 m/s d x = v x t d x = (35 m/s) x (4 s) = 140 m t = 4 s a. Find the height of the cliff. Given Formula Solution t = 4 s d y = 4.9t 2 d y = (4.9) x (4 s) 2 = 78.4 m 2. Repeat the above problem with 5 seconds as the time. 11 Page

12 Class/HomeWork 1. While chasing the Road Runner, Wile E. Coyote makes wrong turn and ends up sliding horizontally off the edge of a high cliff. He leaves the edge of the cliff while traveling with a horizontal velocity of 50 m/s. He hits the bottom 3 seconds later. b. Find the horizontal distance the coyote travels. c. Find the height of the cliff. 2. Billy throws a water balloon off the top of the school in attempt to hit Mr. Beatty. If Billy throws the balloon with a horizontal velocity of 3 m/s and the balloon is in the air for 6 seconds determine the: (a) Horizontal distance the balloon travels. (b) The height of the school. 12 Page

13 3. A monkey throws a banana horizontally at 10 m/s from the top of a tree. The banana hits the ground 6 seconds later. a. How far from the base of the tree does it land? b. How high is the tree? c. How fast was the banana moving vertically (v y ) as it hit the ground? d. How fast horizontally was the banana moving as it hit the ground? 4. A bowling ball rolls off a high cliff at 5 m/s. Complete the chart below that describes its motion during each second it is in the air. Time (s) Horizontal Velocity (m/s) Vertical Velocity (m/s) Horizontal Distance (m) Vertical Distance (m) Page

14 5. Chris throws a water balloon horizontally off the top of the school at 8 m/s attempting to hit his friend s car. The balloon is in the air for 4 seconds before striking the ground. a. How far away is Chris teacher standing? b. What is the height of the high school? c. What is the vertical velocity of the ball just before it strikes the ground? d. What is the horizontal velocity of the ball just before it strikes the ground? 6. A ball is projected horizontally at velocity of 10 m/s from the top of a 50 m high cliff. How high is the ball 2.5 seconds after it is released? 7. A ball is projected horizontally at velocity of 10 m/s from the top of a 50 m high cliff. What is the horizontal distance from the base of the cliff that the object lands? 14 Page

15 Investigation 6A Physics Research Question How can you predict the distance a projectile will travel? Toss a ball some distance and you can imagine in your mind the arc it follows, first rising then falling to the ground. The path the ball follows is the subject of this Investigation. Projectile motion describes objects moving under the influence of gravity, including thrown balls, coasting spacecraft, and even meteors. The range is the horizontal distance a projectile travels between launch and touch down. In this experiment you will see how the range depends on the launch angle. Procedure Part I 1. Set up by marking a tape line on the floor. This line is where you set the front edge of the launcher. 2. One person launches while several group members stand to either side to spot where the marble first touches the ground. 3. Place a marble in the barrel and then pull the pin back and slide it into one of the five slots. 4. Use your thumb to flick the pin out of the slot and launch the marble. 5. Use only the plastic marbles, and follow all safety rules. 6. Spotting the landing point is tricky. It often takes several launches to figure out where the marble lands. Investigate 1. What two variables most affect the range of the marble? (Hint: Both are adjusted on the Marble Launcher) 2. If you wish to study the effect of changing one variable, what must be done with the other one? Procedure Part II 1. Choose which release slot on the barrel of the marble launcher to use for all your range measurements. 2. Measure the range every ten degrees from 10 to 90 degrees, and also at 45 degrees. 15 Page

16 Table 1: Range versus angle data Launch Angle (degrees) Range (meters) Analysis 1. Make a graph with launch angle on the x-axis and range on the y-axis. Use your graph to find the angle that launches the marble with the greatest range. 2. The Marble Launcher starts the marble more than 10 cm above the floor. Suppose the marble were launched from floor level. Do you think it would go a shorter, longer, or about the same distance? Explain why. 3. You are challenged to launch a marble to travel a distance of 3.00 meters. At what angle will you set the launcher? 4. Referring to your answer for question 3, state another angle that would give you the same result. 16 Page

17 The Physics of Golf Physics Research Question How does contact angle affect trajectory and distance? Hypothesis Procedure Part 1. Choose only one golf club to use for all your range measurements. Select an angle of 0 degrees and hit the ball. Record how far (the range) it travels in table 1 below. 2. Measure the range every ten degrees from 10 to 90 degrees, and also at 45 degrees. 3. How does the angle affect the trajectory of the golf ball? 4. How does the angle affect the distance (range) a golf ball is launched? Table 1: Range versus angle data Launch Angle (degrees) Range (meters) Analysis 5. Make a graph with launch angle on the x-axis and range on the y-axis. Use your graph to find the angle that launches the golf ball with the greatest range. 6. You are challenged to launch a golf ball to travel a distance of 200 meters. At what angle will you hit it? 7. Referring to your answer for question 3, state another angle that would give you the same result. 17 Page