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UNIT 2 Two Dimensional Motion And Vectors 1 ConcepTest 3.6c A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed? Dropping the Ball III 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant 2 ConcepTest 3.6c A projectile is launched from the ground at an angle of 30o. At what point in its trajectory does this projectile have the least speed? Dropping the Ball III 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant The speed is smallest at the highest point of its flight path because the ycomponent of the velocity is zero. 3 ConcepTest 3.10a Shoot the Monkey I You are trying to hit a friend with a water balloon. He is sitting in the window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? 1) yes, it hits 2) maybe – it depends on the speed of the shot 3) no, it misses 4) the shot is impossible 5) not really sure Assume that the shot does have enough speed to reach the dorm4 across the street. ConcepTest 3.10a Shoot the Monkey I You are trying to hit a friend with a water balloon. He is sitting in the window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? Your friend falls under the influence of gravity, just like the water balloon. Thus, they are both undergoing free fall in the y-direction. Since the slingshot was accurately aimed at the right height, the water balloon will fall exactly as your friend does, and it will hit him!! 1) yes, it hits 2) maybe – it depends on the speed of the shot 3) no, it misses 4) the shot is impossible 5) not really sure Assume that the shot does have enough speed to reach the dorm5 across the street. ConcepTest 3.10b Shoot the Monkey II You’re on the street, trying to hit a friend with a water balloon. He sits in his dorm room window above your position. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him?? 1) yes, it hits 2) maybe – it depends on the speed of the shot 3) the shot is impossible 4) no, it misses 5) not really sure Assume that the shot does have enough speed to6reach the dorm across the street. ConcepTest 3.10b Shoot the Monkey II You’re on the street, trying to hit a friend with a water balloon. He sits in his dorm room window above your position. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him?? This is really the same situation as before!! The only change is that the initial velocity of the water balloon now has a y-component as well. But both your friend and the water balloon still fall with the same acceleration -- g !! 1) yes, it hits 2) maybe – it depends on the speed of the shot 3) the shot is impossible 4) no, it misses 5) not really sure Assume that the shot does have enough speed to7reach the dorm across the street. Thursday September 29 Projectiles: Launch At Any Angle 8 TODAY’S AGENDA Thursday, September 29 Projectile Motion Mini-Lesson: Launch At Any Angle Hw: Complete Projectile Motion Worksheet p15 UPCOMING… Thurs: More Projectile Motion Problems @ the Boards Fri: Problem Quiz 2 Projectile Motion Access to Reading Quizzes ENDS @ 11:30pm Mon: Problems @ the Boards Tues: CH 3 TEST Wed: Lab 3 Report Due 9 Demonstration with Dr. Walter Lewin Two Dimensional Cannon on Cart 10 Projectile Motion Equations Horizontal Velocity Eq 1 Vertical Velocity Eq 2 Eq 3 Horizontal Displacement Eq 4 11 Projectile Motion Equations Vertical Displacement Eq 5 Range Eq 6 Time to the Top Eq 7 12 Solving Projectile Motion Outline 1) If vi is launched at an angle, break the vi into x- and y- components. 2) If vi is launched at 0° angle, go to step 3. 3) If time of flight is not given, solve for time first. 4) Considering the given information, decide which component equations (x or y) can best solve for time of flight. 5) If the variable you are solving for is in the y-direction, use only the y-component equations. If the variable you are solving for is in the x-direction, use only the x-component equations. 6) Finally, if the projectile begins and ends at the same y-position, you can use the Range equation for what you need. 13 Sample Problem A baseball is thrown with an initial speed of 15.0 m/s. If the ball’s horizontal displacement is 17.6 m, at what angle with respect to the ground is the ball pitched? Ө = 25.1° 14 Sample Problem A football is kicked so that its initial speed is 23.1 m/s. If the football reaches a maximum height of 16.9 m, at what angle with respect to the ground is the ball kicked? Ө = 52.0° 15 Sample Problem Jackie Joyner-Kersee’s record long jump is 7.49 m. Suppose she ran 9.50 m/s to jump this horizontal distance. At what angle above the horizontal did she jump? Ө = 27.3° 16 Sample Problem A ball is thrown from a roof with a speed of 10.0 m/s and an angle of 37.0° with respect to the horizontal. What are the vertical and horizontal components of the ball’s displacement 2.5 s after it is thrown? Δx = 20 m Δy = -16 m 17 Sample Problem A downed pilot fires a flare from a flare gun. The flare has an initial speed of 250.0 m/s and is fired at an angle of 35.0° to the ground. How long does it take for the flare to reach its maximum altitude? t = 15 s 18 Sample Problem In 1991, Doug Danger rode a motorcycle to jump a horizontal distance of 76.5 m. Find the maximum height of the jump if his angle with respect to the ground at the beginning of the jump was 12.0°. Δymax = 4.07 m 19 Sample Problem A scared kangaroo once cleared a fence by jumping with a speed of 8.42 m/s at an angle of 55.2° with respect to the ground. If the jump lasted 1.40 s, how high was the fence? What was the kangaroo’s horizontal displacement? Δx = 6.73 m Δy (fence) = 2.44 m 20 Sample Problem Measurements made in 1910 indicate that the common flea is an impressive jumper, given its size. Assume that a flea’s initial speed is 2.2 m/s, and that it leaps at an angle of 21° with respect to the horizontal. If the jump lasts 0.16 s, what is the magnitude of the flea’s horizontal displacement? How high does the flea jump? Δx = 0.33 m Δy = 0.032 m 21 END 22