Horizontal Projectiles 2-Dimensions Did you watch the video? http://aplusphysics.com/courses/regents/videos/Projectiles_Regents/Projectiles_Regents.html http://aplusphysics.com/courses/regents/videos/Horizontal_Projectiles/Horizontal_Projectiles.html
A projectile is ONLY acted on by one force- GRAVITY Neglect air resistance Path of a projectile is PARABOLIC Symmetry of motion (like “throw up” problems)- tup = tdown .This will become important when we do projectiles at an angle. Independence of motion- 2 dimensions: Vertical (y)- freefall Horizontal (x)- 0 acceleration/constant velocity
Review Horizonal Movement: Let’s look at a car moving east on a frictionless surface at a constant velocity of 20 m/s. Evenly spaced dots = constant velocity How far will this car go in 5 s?
Review Freefall (vertical movement): A ball is dropped from rest at a height of 80m above the ground. How long does it take to reach the ground? What’s its velocity just before it hits the ground?
Projectiles are both horizontal and vertical movement…but they are treated separately. There is NO force pulling the cannon horizontally = CONSTANT VELOCITY What is the only force acting on the cannon? THE FORCE OF GRAVITY = ACCELERATION
Path is NOT straight. Path is parabolic. Eventually the path will go straight down because air resistance will slow the object in the x (horizontal) direction.
both bullets downward in the vertical direction is gravity. Bullet Fired vs. Bullet Dropped Neglecting air resistance a bullet “dropped” at the same height and time as another is horizontally fired will both hit the ground at the same time. The ONLY force pulling both bullets downward in the vertical direction is gravity. https://www.youtube.com/watch?v=D9wQVIEdKh8
The x and y components are independent of each other The x and y components are independent of each other. The only thing they have in common is time. x y vi = vf = ax = ay = dx (range) = dy (height) = time = If you know time you can connect one dimension of motion to the other!
Finding t, vfy and dx: Matt kicks a soccer ball at 12 m/s horizontally from the edge of the roof of a building which is 45 m high. a. When does it strike the ground? b. What is the final velocity in the vertical direction? c. How far away from the building does the soccer ball land? 12 m/s 45 m d =?
Finding vix: 2. A car drives straight off the edge of a cliff that is 180 m high. The police at the scene of the accident note that the point of impact is 240 m from the base of the cliff. How fast was the car traveling when it went over the cliff? x y vi = vf = ax = ay = dx (range) = dy (height) = time =
Finding t and dx: 3. A Plane flying horizontally at an altitude of 500 meters and having a velocity of 250 m/s east, drops a supply packet to a work crew on the ground. It falls freely without a parachute. Assume no wind and negligible air resistance. Determine the time required for the packet to hit the ground. Determine the horizontal distance from the target area that the plane must drop the packet.
Revisit: vix = 12 m/s Matt kicks a soccer ball at 12 m/s horizontally from the edge of the roof of a building which is 45 m high. a. When does it strike the ground? b. What is the final velocity in the vertical direction? c. How far away from the building does the soccer ball land? d. With what velocity does the ball strike the ground? 45 m 3 s 30 m/s vix =12 m/s 36 m d =? viy =30 m/s This is going to be the resultant of the horizontal and vertical velocity vectors- Remember vector addition- tip to tail
vix =12 m/s viy =30 m/s a2 + b2 = c2 vix =12 m/s (12 m/s)2 + (30m/s)2 = c2 144 m2/s2 + 900 m2/s2 = 1044 m2/s2 c2 = 1044 m2/s2 c = 32 m/s
Orange Book
x y vix = viy = vfx = vfy = ax = ay = dx (range) = dy (height) = time =
x y vi = vf = ax = ay = dx (range) = dy (height) = time =
x y vi = vf = ax = ay = dx (range) = dy (height) = time =
x y vi = vf = ax = ay = dx (range) = dy (height) = time =