An object launched into space without motive power of its own is called a projectile.

a

PROJECTILE MOTION CHARACTERISTICSThe projectile has:• a constant horizontal velocity and • a vertical velocity that changes uniformly under the influence of gravity.

 If an object is projected horizontally, its motion can best be described by considering its horizontal and vertical motion separately. In the figure we can see that the vertical velocity and position increase with time as those of a free-falling body.

Note that the horizontal distance increases linearly with time, indicating a constant horizontal velocity.

Take this basketball shot as an example.  Notice the horizontal velocity of the ball.  Look at the spacing of the vertical lines which mark the position of the ball every 10th of a second.  The spacing is quite consistent, which indicates a constant horizontal velocity. 

HORIZONTAL MOTION

Velocity (vx) is constant

Velocity    

Distance   

Time    

xx v t

x

xv

t

x

xtv

VERTICAL MOTION

Velocity (vy) increases under the acceleration due to gravity.

Velocity   

Distance    

Time    

0oyv yv gt

21

2y gt

2yt

g

RESULTANT VELOCITY

The resultant velocity can be found using the Pythagorean theorem.

2 2( ) ( )R x yv v v

3.6 A ball is thrown horizontally with a velocity of 12 m/s. How far has the ball fallen 2 s later?

HORIZONTALvox = 12 m/s

t = 2 s

VERTICALvoy = 0 m/sg = 9.8 m/s2

t = 2 s

vox = vx x = vx t

= 12(2) = 24 m

y = ½ gt2

= ½ (9.8)(2)2

= 19.6 m

3.7 A rifle with a muzzle velocity of 200 m/s is fired with its barrel horizontally at a height of 1.5 m above the ground. a. How long is the bullet in the air?

HORIZONTALvox = 200 m/s

g

yt

2

8.9

)5.1(2 = 0.55 s

VERTICALvoy = 0 m/s

y = 1.5 mg = 9.8 m/s2

21

2y gt

b. How far away from the rifle does the bullet strike the ground?

x = vx t

= 200(0.55) = 110 m

3.8 A ball is rolled off the edge of a table 1 m high with a horizontal velocity of 1.8 m/s. With what velocity does it strike the floor?

HORIZONTALvox = 1.8 m/s

We need to find the resultant velocity:22yxf vvv

Where: vx = vox = 1.8 m/s

vy = voy + gt

g

yt

2

8.9

)1(2 = 0.45 s

VERTICALvoy = 0 m/s

y = 1 mg = 9.8 m/s2

21

2y gt

vy = 0 + 9.8(0.45)

= 4.4 m/s

22 )4.4()8.1( fv = 4.75 m/s

THE MONKEY AND THE ZOOKEEPER

The monkey spends most of its day hanging from a branch of a tree. The zookeeper feeds the monkey by shooting bananas from a banana cannon to the monkey in the tree. The monkey usually drops from the tree the moment that the banana leaves the muzzle of the cannon. The zookeeper is faced with the dilemma of where to aim the banana cannon in order to feed the monkey. If the monkey lets go of the tree the moment that the banana is fired, then where should he aim the banana cannon?

The zookeeper aims above the monkey (perhaps he presumes that gravity will accelerate the banana downward such that it hits the monkey). What would be the path of the banana? Would the banana hit the monkey?

Since both banana and monkey experience the same acceleration each will fall equal amounts and the banana misses the monkey, moving over his head.

Wrong move!

The zookeeper aims at the monkey and shoots the banana.

Since both banana and monkey experience the same acceleration each will fall equal amounts the banana reaches the monkey!

The key to the zookeeper's dilemma is to aim directly at the monkey.

SHOOT THE MONKEY

Happy monkey!