By Corina Bot

Kinematic Equations and Projectile Motion

Projectile Motion

The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration g.This photograph shows two balls that start to fall at the same time. The one on the right has an initial speed in the x-direction. It can be seen that vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly.wikipedia.org

- Package follows a parabolic path and remains directly below the plane at all times.

- As the package falls, it undergoes a vertical acceleration; there is a change in its vertical velocity.

- This vertical acceleration is attributed to the downward force of gravity which acts upon the package.

http://www.physicsclassroom.com/

- A cannonball being launched at an angle from a cannon atop of a very high cliff.- The cannonball follows a parabolic path.- As the cannonball rises towards its peak,

it undergoes a downward acceleration. An upwardly moving cannonball which is slowing down is said to be undergoing a downward acceleration.

Kinematic Equations for Constant Acceleration in Two Dimensionsx Component (horizontal) y Component (vertical)

vx = vxo + axt vy = vyo + aytx = xo + vxot + ½ axt2 y = yo + vyot + ½ ayt2

vx = vxo + 2ax(x – xo) vy = vyo + 2ay(y – yo)

v0x

v0y

vq0

http://www.physicsclassroom.com/

A child sits upright in a wagon which is moving to the right at constant speed as shown. The child extends her hand and throws an apple straight upward (from her own point of view), while the wagon continues to travel forward at constant speed. If air resistance is neglected, will the apple land (a) behind the wagon, (b) in the wagon, or (c) in front of the wagon?

Conceptual Example 3-6/pag. 59: Where does the apple land?

"Physics" by Giancoli, 6th ed.

A child sits upright in a wagon which is moving to the right at constant speed v0=20m/s, as indicated. The child extends her hand and throws an apple at an angle a = 27⁰, while the wagon continues to travel forward at constant speed. If air resistance is neglected, calculate distance traveled by the cart until apple reaches back the child’s hand.

22

2

1sin

2

10

cos

tgtvtgtvy

tvtvdx

ooy

oox

t = ?d = ?

Particular equationsd=?

v0x

v0yv0

a x

y

time = t

General equations

20

0

2

1tatvy

tvx

y

x

v0=20m/s

a = 27⁰

d = ?

22

2

1sin

2

10

cos

tgtvtgtvy

tvtvdx

ooy

oox

t = ?d = ?

Particular equations

)1(82.17

27cos20

cos

cos

ts

md

ts

md

tvd

tvtvdx

o

oox

From horizontal (x) equation:

st

t

t

ttt

ts

mt

s

m

tgtv

tgtvtgtvy

o

ooy

85.1

07.99.4

09.407.9

:09.407.9

08.92

127sin20

02

1sin

2

1sin

2

10

2

22

2

22

From vertical (y) equation:

Substitute t in equation (3) to get d:

md

ss

md

ts

md

9.32

8.182.17

82.17

d=?v0x

v0yv0

a x

y

time = t

v0=20m/s

a = 27⁰

d = ?