projectile motion diagram
DESCRIPTION
Projectile motion diagram. Questions concerning previous slide. What is the point of this picture?. vx & vy are independent. Determining final velocity. Determining muzzle velocity. Questions concerning previous slide. What does each of the following designate? - PowerPoint PPT PresentationTRANSCRIPT
Projectile motion diagram
Questions concerning previous slide
What is the point of this picture?
vx & vy are independent
Determining muzzle velocity
Determining final velocity
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
vox
· vox = the initial velocity in the horizontal direction.
· vox = muzzle velocity of, in this case, the cannon
Vx
· vx is the final velocity in the horizontal direction or the velocity @ any point in time in the horizontal direction.
voy
· Voy is the initial velocity of the projectile in the vertical direction.
vy
· vy is the final velocity in the vertical direction or the velocity in the vertical direction @ any point in time.
dx
dx is the distance traveled by the projectile in the horizontal direction. Also called “range” & sometimes designated “R”.
dy
· dy is the heighth from which the projectile is fired or the vertical distance the projectile falls.
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.
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).
Value of voy
· voy = 0 since the cannonball was projected horizontally.
Values
Value of vy
· vy = voy2 + 2gdy
· Do you understand how we
arrived @ this?
Value of vox & vx
• vx = vox = dx/tx
Value of v
·v = vx + vy
· i.e. the vector sum
· vx & vy = rectangular form· v = polar form
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
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
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.
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
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
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
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
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
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!
Ballisitics
· The study of projectile motion which considers all forces working on a projectile -- that is, it considers air resistance as well as gravity.
Key concept
· The velocity in the vertical direction is unaffected by what is happening in the horizontal direction.