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.