Projectile motion

Free-falling while moving horizontally

Moving in two directions at the same time

Projectile motion

Parabolic trajectory

Vertical motion: with acceleration of -9.8 m/s2 and initial velocity vy and vertical displacement Δy Horizontal motion: constant vx and horizontal displacement Δx

Projectile motionVertical HorizontalAccelerated Constant speed

2

2

2 2

vertical componen

9.8 /

1 ( )

t

22

f i

i

f i

tt

t

v

vg m s

v v g

y v t g

v v g y

horizontal component

i f

xv

v v v

x vxt

vv

t

t

An object launched horizontally

Find the initial speed of the bikeGiven Equations / Substitution Solving

Horizontal Vertical

Lab – Launching a Projectile Horizontally

• Work in pairs• Each person should have his / her set of data• Each student turns in a report with his / her

name on it.

Projectile Launched at an angle

Projectile has initial velocity in both directions

Example

• A football is kicked 22 m/s at 40o to the horizontal. Calculate the maximum height and horizontal range the football will reach before it falls down (providing no one catches it).

1st step:

2 2

2

2 ( 0)

2

f i f

i

H y

v v g y v

vy

g

?

R xx v tt

0 14 9.8

vg tt

2 1.44 2.9( )t s

17 2.8 49( )R m

Example 2 (p.110, #35)

• A place kicker must kick a football from a point 36.0 m from the goal. As a result of the kick, the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53° to the horizontal.

• a. By how much does the ball clear or fall short of clearing the crossbar?

• b. Does the ball approach the crossbar while still rising or while falling?

Given Units Equations Substitute/Solve