Aim: How can we solve problems dealing with horizontally fired

objects?

Do Now:

An object falls freely for 75 m. How long does it take to reach the ground? How fast is it moving upon impact?

d = vit + ½at2

-75 m = (0 m/s)t + ½(-9.8 m/s2)t2

t = 3.9 s

vf = vi + at

vf = (0 m/s) + (9.8 m/s2)(3.9 s)

vf = 38.3 m/s

Demo

A bullet is shot out horizontally from a gun. At the same time and from the same height, a second bullet is dropped to the ground. Which hits the ground first?

They hit at the same time!

What goes on vertically has no impact as to what goes on horizontally

What do you notice about the horizontal motion and the vertical motion?

Used for problems such as:Used for problems such as: Horizontally fired objects such as Horizontally fired objects such as

bullets, cars driving off of cliffs, bullets, cars driving off of cliffs, etc.etc.

Dropping an object while Dropping an object while moving, such as a bomb or moving, such as a bomb or humanitarian package.humanitarian package.

The shape of the path is a The shape of the path is a parabolaparabola

Car off Cliff

Separate ComponentsSeparate Components Velocity, acceleration, and Velocity, acceleration, and

distance have both distance have both horizontal (x) component, horizontal (x) component, and vertical (y) componentand vertical (y) component

Horizontal ComponentsHorizontal Components Horizontal velocity is constant:Horizontal velocity is constant:

vvv fi There is no horizontal acceleration:There is no horizontal acceleration:

Horizontal distance (also known as the Horizontal distance (also known as the rangerange) is found using this equation:) is found using this equation:

a = 0 m/s2

t

dv

Vertical ComponentsVertical Components For the vertical motion, the object is in free For the vertical motion, the object is in free

fall:fall:

Vertical acceleration = gravity:Vertical acceleration = gravity:

Vertical distance (also known as the Vertical distance (also known as the heightheight) is found using the distance ) is found using the distance equation:equation:

vi = 0 m/s

a = g = -9.8 m/s2

d = vit + ½at2

TimeTime Vertical and Horizontal Vertical and Horizontal time are equal:time are equal:

yx tt

Separate your information according to vertical and horizontal

x y

v vi = 0 m/s

a = -9.8 m/s2

d =height

d = range

t = t

ExampleExample

Thelma and Louise drive off a cliff 75 m Thelma and Louise drive off a cliff 75 m high with a speed of 15 m/s.high with a speed of 15 m/s.

How long does it take to hit the How long does it take to hit the ground?ground?

x y

smv /15 vi = 0 m/s

a = -9.8 m/s2

d = -75 m

t = ?

t = ?

Determine which column you have enough information so that you can solve the problem.

The vertical column has enough.

Do not mix and match vertical and horizontal information!!!

d = vit + ½at2

-75 m = (0 m/s)t + ½(-9.8 m/s2)t2

-75 = -4.9t2

15.3 = t2

3.9 s = t

HowHow far from the base of the cliff do they land?far from the base of the cliff do they land?

x y

smv /15 vi = 0 m/s

a = -9.8 m/s2

d = -75 m

t = 3.9 s

t = 3.9 s

d = ?

t

dv

s

dsm

9.3/15

d = 58.5 m

How fast are they traveling vertically on impact?How fast are they traveling vertically on impact?

x y

smv /15 vi = 0 m/s

a = -9.8 m/s2

d = -75 m

t = 3.9 s

vf = ?

t = 3.9 s

d = 58.5 m

vf = vi + at

vf = (0 m/s) + (-9.8 m/s2)(3.9 s)

vf = -38.3 m/s

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