Projectile motion/Type 1 and 2

Projectile motion is the motion of an object whose path is affected by the force of gravity. We are all affected by gravity, but it profoundly alters the motion of objects that are thrown or shot upward. The arching of a thrown ball is caused by gravity, as well as its falling motion in general.

When faced with a projectile motion problem, there are things you must do and remember.

Do
1. determine the horizontal and vertical components of the initial velocity.


For an object projected horizontally, the vertical component of initial velocity is zero.
For an object thrown at 20 m/s 53º above the horizontal, the vertical component of the initial velocity is 20sin53º = 16.0 m/s [up], and the horizontal component is 20cos53º = 12.0 m/s.

2. break down the problem into two problems: horizontal and vertical.
3. assign - and + signs appropriately

Remember:
1. acceleration is zero in the horizontal component and g in the vertical.
2. at the top of its rise, the projectile has a vertical velocity = zero.

(For the two types of projectile motion below, I had to defy Mr. Chung's use of certain letters for certain values because the diagrams that I found used different letters.)

TYPE 1

x-components

1. Component of initial velocity along x-axis.
u_x=u

2. Acceleration along x-axis
a_x=0
(Because no force is acting along the horizontal direction)

3. Component of velocity along the x-axis at any instant t.
v_x=u_x + a_xt
=u + 0

» v_x=u
This means that the horizontal component of velocity does not change throughout the projectile motion.
4. The displacement along x-axis at any instant t
x=u_xt + (1/2) a_xt²
» x=u_xt + 0
» x=u t

y-components

1. Component of initial velocity along y-axis.
u_y=0
2.Acceleration along y-axis
g=9.8m/s²
3. Component of velocity along the y-axis at any instant t.
v_y=u_y + a_yt
=0 + gt
» v_y=gt
4. The displacement along y-axis at any instant t
y= u_yt + (1/2) a_yt²
» y= 0 + (1/2) a_yt²
» y=1/2gt<sup>2

TYPE 2</sup>

                                                                     x-components

1. Component of initial velocity along x-axis.
u_x=u cosØ  [Ø = theta]

2. Acceleration along x-axis
a_x=0
(Because no force is acting along the horizontal direction)

3. Component of velocity along the x-axis at any instant t.
v_x=u_x + a_xt
=ucosØ + 0

= ucosØ

» v_x=ucosØ
This means that the horizontal component of velocity does not change throughout the projectile motion.
4. The displacement along x-axis at any instant t
x=u_xt + (1/2) a_xt²
» x=(ucosØ)t

y-components

1. Component of initial velocity along y-axis.
u_y=u sinØ
2.Acceleration along y-axis
g= -9.8m/s²
3. Component of velocity along the y-axis at any instant t.
v_y=u_y + gt
v_y=usinØ + gt
 4. The displacement along y-axis at any instant t
y= u_yt + (1/2) gt²
» y= (usinØ)t + (1/2)gt²