3 projectile motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • angled...
TRANSCRIPT
![Page 1: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/1.jpg)
Projectile Motion
![Page 2: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/2.jpg)
Conceptual Challenge
Which boat:
• Q1. Has the highest speed?
• Q2. Takes the least time to cross the river?
• Q3. Travels the shortest distance?
![Page 3: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/3.jpg)
Conceptual Challenge
Which boat:
• Q1. Has the highest speed?
• Q2. Takes the least time to cross the river?
• Q3. Travels the shortest distance?
C, Greatest Resultant
A, Greatest Velocity in the x-dir
B, Resultant is directly across the path
![Page 4: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/4.jpg)
Announcements
• Lab is due tomorrow - Please email it to me instead of printing it. [Word or PDF file]. Deadline is 10:30AM tomorrow (4th period). Any emails received after 10:30AM are considered late
![Page 5: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/5.jpg)
2-D Kinematics
• Relative Motion
• Projectile Motion
• Angled Projectiles
![Page 6: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/6.jpg)
![Page 7: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/7.jpg)
Which forces are acting in the x and y directions? [Neglect air resistance]
![Page 8: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/8.jpg)
Which forces are acting in the x and y directions? [Neglect air resistance]
• Y-direction: Net force = gravity -> gravitational acceleration (ay = -9.8m/s/s)
• X-direction: No net force -> no acceleration (ax = 0 m/s/s; neglect air resistance)
![Page 9: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/9.jpg)
X and Y have no effect on each other!
![Page 10: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/10.jpg)
![Page 11: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/11.jpg)
The time it takes to fall depends on height, not horizontal
velocity [tennis ball example]
We can agree on the time it takes to go up and down
![Page 12: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/12.jpg)
![Page 13: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/13.jpg)
Step 1: GivensX-direction Y-direction
Vx = 4.5 m/s ∆x = ? ∆y = -7.5m
![Page 14: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/14.jpg)
Step 1: GivensX-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
![Page 15: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/15.jpg)
Step 2: Equations that might help?
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
![Page 16: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/16.jpg)
Step 2: Equations that might help?
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
Vx = ∆x/t -> ∆x = Vx*t
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
![Page 17: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/17.jpg)
Step 2: Equations that might help
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
Vx = ∆x/t -> ∆x = Vx*t
we need time!
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
![Page 18: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/18.jpg)
Step 2: Equations that might help
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
Vx = ∆x/t -> ∆x = Vx*t
we need time!
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
time is the same for x and y!
![Page 19: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/19.jpg)
Step 2: Equations that might help
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
Vx = ∆x/t -> ∆x = Vx*t
we need time!
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
Let’s look for time first: t = ?
![Page 20: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/20.jpg)
Step 3: Calculations
![Page 21: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/21.jpg)
∆y = Vo,y*t + (1/2)at2
[Note: Vo,y = 0 m/s]
∆y = Vo,y*t + (1/2)at2
∆y = (1/2)at2
t = √[(2∆y)/a]
t = √[(2(-7.5m)/(-9.8m/s2]
t = 1.24s
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s
Let’s look for time first:
t = ?
![Page 22: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/22.jpg)
Step 2: Equations that might help
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
Vx = ∆x/t -> ∆x = Vx*t
we need time!
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s t = 1.24s
![Page 23: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/23.jpg)
Step 2: Equations that might help
X-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
t = 1.24s
Vx = ∆x/t -> ∆x = Vx*t
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s t = 1.24s
![Page 24: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/24.jpg)
Step 2: Equations that might helpX-direction (Const. vel) Y-direction (Free fall)
Vx = 4.5 m/s ∆x = ?
t = 1.24s
-> ∆x = Vx*t ∆x = (4.5m/s)(1.24s)
= 5.6m
Done!
∆y = -7.5m ay = -9.8 m/s/s
Vy,o = 0 m/s t = 1.24s
![Page 25: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/25.jpg)
Recap1. List out everything in a table (X,Y)
2. We wanted ∆x but we needed time
3. time is the same in x+y, so we solved it in the other axis
4. once we had time, we plugged in to original problem
![Page 26: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/26.jpg)
Practice
![Page 27: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/27.jpg)
Assume a horizontal launch.
![Page 28: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/28.jpg)
t = 1.75
∆x = 35m
![Page 29: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/29.jpg)
1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile?
b. How far away from the bottom of the ledge does the ball land?
![Page 30: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/30.jpg)
1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile?
2.02 s
b. How far away from the bottom of the ledge does the ball land? 50.5 m
![Page 31: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/31.jpg)
2. A bomb is released from a plane flying level at an altitude of 20000 m. It lands 40000 m horizontally from where it was released. a. How long was the bomb in the air?
b. What was the plane's speed when the bomb was released?
![Page 32: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/32.jpg)
2. A bomb is released from a plane flying level at an altitude of 20000 m. It lands 40000 m horizontally from where it was released. a. How long was the bomb in the air? 63.89 s
b. What was the plane's speed when the bomb was released? 626.1 m/s
![Page 33: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/33.jpg)
3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff?
b. How far away does the stone hit the ground?
![Page 34: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/34.jpg)
3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff? 988 m
b. How far away does the stone hit the ground? 355 m
![Page 35: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/35.jpg)
4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the
water below?
b. How far from the base of the bridge will it hit?
![Page 36: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/36.jpg)
4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the
water below? 5.53 s
b. How far from the base of the bridge will it hit? 33.2 m
![Page 37: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/37.jpg)
5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air?
b. How high was it thrown from?
![Page 38: 3 Projectile Motionpaguayphysics.weebly.com/uploads/8/8/9/0/88908304/3_projectile_… · • Angled Projectiles. Which forces are acting in the x and y directions? [Neglect air resistance]](https://reader035.vdocument.in/reader035/viewer/2022063003/5f6e435ba95964743b78760a/html5/thumbnails/38.jpg)
5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air? 3 s
b. How high was it thrown from? 44 m