Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx...
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![Page 1: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/1.jpg)
Projectile motion diagram
Questions concerning previous slide
What is the point of this picture?
vx & vy are independent
Determining muzzle velocity
Determining final velocity
![Page 2: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/2.jpg)
Questions concerning previous slide
1) What does each of the following designate?
vox, vx, voy, vy, dx, dy, v? Say it in words.
2) Why does vx = vox?
3) What is the value of voy?
4) What is the value of vy?
5) What is the value of vox & vx?
6) What is the value of v?
Diagram
![Page 3: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/3.jpg)
vox
· vox = the initial velocity in the horizontal direction.
· vox = muzzle velocity of, in this case, the cannon
![Page 4: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/4.jpg)
Vx
· vx is the final velocity in the horizontal direction or the velocity @ any point in time in the horizontal direction.
![Page 5: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/5.jpg)
voy
· Voy is the initial velocity of the projectile in the vertical direction.
![Page 6: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/6.jpg)
vy
· vy is the final velocity in the vertical direction or the velocity in the vertical direction @ any point in time.
![Page 7: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/7.jpg)
dx
dx is the distance traveled by the projectile in the horizontal direction. Also called “range” & sometimes designated “R”.
![Page 8: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/8.jpg)
dy
· dy is the heighth from which the projectile is fired or the vertical distance the projectile falls.
![Page 9: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/9.jpg)
v
· v = the final velocity of the projectile just before it strikes the ground or the velocity of the projectile @ any point in time. That is, polar form of the vector w/ vx & vy being the rectangular form.
![Page 10: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/10.jpg)
vx = vox
· vx = vox b/c there is no acceleration in the horizontal direction if we neglect air resistance (which is negligible with a cannonball or for any projectile over short vertical falls).
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Value of voy
· voy = 0 since the cannonball was projected horizontally.
![Page 12: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/12.jpg)
Values
Value of vy
· vy = voy2 + 2gdy
· Do you understand how we
arrived @ this?
Value of vox & vx
• vx = vox = dx/tx
![Page 13: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/13.jpg)
Value of v
·v = vx + vy
· i.e. the vector sum
· vx & vy = rectangular form· v = polar form
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What is the point of this picture?
· Also se fig. 6-1 p. 148 of your text, essentially the same picture.
· This picture depicts a device that shoots & drops 2 balls simultaneously.
· Projectile motion diagram
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vx & vy are independent
· The velocity in the vertical direction is unaffected by what is happening in the horizontal direction. Return to the previous slide & notice that the vertical posn. of the projected ball & dropped ball is always the same!
· Projectile motion diagram
Last slide
![Page 16: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/16.jpg)
vx & vy
· Velocity in the horizontal direction is constant.
· Velocity in the vertical direction is inconstant, vy ≠ voy. Velocity in the vertical direction varies in accordance w/ g & time.
![Page 17: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/17.jpg)
Determining muzzle velocity
Muzzle velocity is the velocity w/ which a bullet emerges from the barrel of a gun.
· vox = vx
· & vx = dx/tx
· Therefore, we must know dx & tx
· dx can be measured.
Projectile motion diagram
![Page 18: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/18.jpg)
Determining muzzle velocity - cont.
5) & tx = ty
How fast something falls is independent of vo. This is true as long as vo is totally in the x direction i.e. voy
= 0.
Projectile motion diagram
![Page 19: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/19.jpg)
It may appear to be affected less when moving @ faster speeds but this is only
b/c of the vx/vy ratio
1) Since tx = ty
2) ty = ?
3) dy = voyt + 1/2 gty2
4) ty = 2dy/g
5) Not we can calculate vx.
vx = dx/tx
Projectile motion diagram
![Page 20: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/20.jpg)
Determining final velocity
· v = vx + vy
· vx - calculated on previous slides
· vy can be calculated (instant before it hits the ground).
· vy2 = voy
2 + 2gdy
· vy = 2gdy· Projectile motion diagram
![Page 21: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/21.jpg)
Determining final velocity - cont.
· tan = vy/vx
· Magnitude:
· cos = vx/v or sin vy/v
· v = vx/cos or v = vy/sin
· Better yet since we know vx & vy Simply R->P
· Projectile motion diagram
![Page 22: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/22.jpg)
Air resistance
· So far air resistance has not been considered.
· There are 2 ways air resistance affects projectile motion.
1) Decrease vx
2) Decrease vy
• Think about it!
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Ballisitics
· The study of projectile motion which considers all forces working on a projectile -- that is, it considers air resistance as well as gravity.
![Page 24: Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c0301a28abf838cdaf38/html5/thumbnails/24.jpg)
Key concept
· The velocity in the vertical direction is unaffected by what is happening in the horizontal direction.