Motion in a Plane

 

I. 2-D Motion & Trajectories

What kinds of objects have 2 dimensional motion?

 

 

 

Objects moving
along earth's surface

Planets around sun

Pendulums


Projectiles

A) Objects moving along earth’s surface (projectiles)

1. Projectile fired horizontally

Dropped/Projected Horizontally Rutgers U.

1. Viy = ?

 

 

Viy = 0

 

 

2. ay = _____

 

 

ay = 9.8 m/s2

 

3. Horizontal velocity is ________(no air friction)

 

 

 

Horizontal velocity is constant (no air friction) 

 

Vix = Vx = constant

Horizontal Distance traveled

dx = Vxt
(Memorize)

 

 

 

4 objects thrown horizontally, same height, at various speeds.

Compare their:

 

 

 

Viy?



Same
Viy = 0



ay?





Same
ay = 10 m/s2




Vy?




Same
at all times




height (dy)?




Same
at all times



time spent in air




same

 

 

 

 

Object is thrown horizontally, only one factor determines the time in air. 

 

 

 

 

Object's initial height

 

 

 

 

 

 

 

Which ball remains
in flight the longest?

June 1997 #64

 

 

 

 

Choice 4 - (greatest height)

 

 

B) Projectile fired horizontally - Solving Word Problems

 

Ex) A baseball is thrown horizontally from a grandstand 20 m above ground at speed of 10m/s.

(a) How long will the ball remain in flight before reaching ground?

 

 

 

 

Ex) A baseball is thrown horizontally from a grandstand 20 m above ground at speed of 10 m/s.

 

(a) How long will the ball remain in flight before reaching ground?

 

 

Horizontal Info Vertical Info
Vx = 10 m/s Viy = 0
(thrown horizontally)
  ay = +9.8 m/s2
  dy = 20 m
  t = ?

 

Step 3 - Substitute and Solve

dy = Viyt + ½ayt2

 

20 m = 0 + ½(9.8 m/s2)t2
 

t = 2 seconds


(b) What is the projectile's maximum range before it hits ground?

 

 

(b) What is the projectile's maximum range before it hits ground?

 

Range?

Horizontal Vertical
Vx = 10 m/s Viy = 0
(thrown horizontally)
dx = ? ay = +9.8 m/s2
  dy = 20 m
  t = 3 sec

 

Range
horizontal displacement (dx)

 

dx =Vxt=(10m/s)2 secs

= 20 m