This document discusses projectile motion, including motion in two dimensions for objects launched horizontally as well as objects launched at an angle. It provides equations to describe the horizontal and vertical components of velocity and position over time for projectiles. An example problem is also given to calculate the velocity, position, and graphs of motion for an object sliding off a table.

1. Projectile Motion
Motion in two dimensions

2. Source: 12th University Physics with ModernPhysics by Young andFreedman
Horizontally launched
projectile
𝑣𝑖𝑥 = 𝑣 𝑓𝑥
𝑣𝑖𝑦 = 0

3. http://onlinephys.com/projectile5.jpg
How does v affect the
horizontal displacement?
How do the x and y
components of v change?

4. Example
An object slides off a horizontal table top with a speed of 1.10m/s. It strikes
the floor in 0.350s. Ignore air resistance. Find:
a. The height of the table top above the floor;
b. The horizontal distance from the edge of the table to the point where
the object strikes the floor;
c. The horizontal and the vertical components of the object’s velocity and
the magnitude and direction of its velocity just before the object
reaches the floor;
d. Draw the x-t, y-t, vx-t, and vy-t graphs for the motion.

5. http://www.met.reading.ac.uk/pplato2/h-flap/phys2_2f_2.png
Projectiles
launched at an
angle

6. Free-body diagram
https://1fdb22f4487524f6c4d9c4d1d58992c57d826129.googledrive.com/host/0BwIiOGYC7-g -OHJURXRkOG9wWVE/fiznotes/chapter7/Block%20on%20ramp%20diagram.png

7. Source: 12th University Physics with ModernPhysics by Young andFreedman
𝑥 = 𝑣𝑖 𝑐𝑜𝑠𝛼𝑖 𝑡
𝑦 = 𝑣𝑖 𝑠𝑖𝑛𝛼𝑖 𝑡 −
1
2
𝑔𝑡2
𝑣 𝑓𝑥 = 𝑣𝑖 𝑐𝑜𝑠𝛼𝑖
𝑣 𝑓𝑦 = 𝑣𝑖 𝑠𝑖𝑛𝛼𝑖 − 𝑔𝑡
𝑣 = 𝑣 𝑥
2 + 𝑣 𝑦
2
tan 𝛼 =
𝑣 𝑦
𝑣 𝑥

8. Source: 12th University Physics with ModernPhysics by Young andFreedman
Projectile launched at an angle

9. http://www.met.reading.ac.uk/pplato2/h-flap/phys2_2f_17.png
How do the x and y components
of v change?
How do the x and y components
of v affect the range and the
height respectively?

10. How does
jumping
before
releasing
the ball
affect the
trajectory?
http://4.bp.blogspot.com/--RoOTPcrhfE/UIZ8SdBh_pI/AAAAAAAAABE/pDOupT8zQRI/s1600/404644_3131260688121_1960337289_n.jpg

11. https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A417ea4c8b5c767653664d24b567a337f3280daaf2fe2dc1cbfd02f42%2BIMAGE%2BIMAGE.1 http://i.dailymail.co.uk/i/pix/2015/02/23/25FD31CB00000578-0-image-a-119_1424703192090.jpg

12. https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Newton_Cannon.svg/2000px-Newton_Cannon.svg.png https://upload.wikimedia.org/wikipedia/commons/6/69/Delta_IV_Medium_Rocket_DSCS.jpg http://www.nasa.gov/sites/default/files/thumbnails/image/arm_space.png
The Plan The Execution The Target position

13. http://www.wallpaperup.com/uploads/wallpapers/2012/12/18/25696/268a082706be203634d33e49cc96e8a3.jpg
240 m/s
θ = 40°