Object Propelled Horizontally - Projectile Motion

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Objects launched horizontally undergo projectile motion: a constant horizontal velocity and an accelerating vertical velocity, acting completely independently of each other.

A 10 kg object is dropped from the same height as a 20 kg object. Compare the time they take to hit the ground.

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Object Thrown Horizontally

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How many velocities?

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2 velocities

Horizontal velocity — Determined by thrower

Vertical velocity — ??????

…acceleration due to gravity

b. Objects Propelled Horizontally

- have 2 velocities V_x, V_y

- V_x is determined by thrower

- V_x constant (neglect friction)

- V_iy = 0 (initial vert. vel.)

- V_y changed by … force of gravity

Ex) Object Thrown Horizontally at 4 m/s

time (sec)	V_x (m/s)	V_y (m/s)
0	4	0
1	4	10
2	4	20
3	4	30

Object Dropped / Object Thrown Horizontally

Comparing an object dropped versus thrown horizontally

Same:

a) a_y (+10 m/s²)

b) vertical drop — d_y

c) time in air

d) same V_y

Compare each sphere's:
A) height above the ground
B) time in the air

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Compare the time it takes for the marbles to hit the ground.

Dropped/Projected Horizontally
Rutgers U

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Ex 1a

Given

A rock is thrown horizontally from the top of a cliff @ 150 m/s.
a) How long does it take the rock to fall 45 m vertically?

Horizontal	Vertical
V_x = 150 m/s	V_iy = 0 (thrown horizontally)
t = ?	a_y = +9.8 m/s²
	d_y = 45 m
	t = ?

↓

Δd_y = V_iyt + ½a_yt² → 45 m = 0 + ½(9.8 m/s²)t² → 45 = 4.9t² → 9 = t²

t = 3 seconds

Ex 1b

Given

Same rock, thrown horizontally from the top of a cliff @ 150 m/s.
b) Find the rock's vertical velocity at 45 meters.

Horizontal Info	Vertical Info
V_x = 150 m/s	V_iy = 0 (thrown horizontally)
	a_y = +9.8 m/s²
	d_y = 45 m
	V_fy = ?

Vfy squared equals Viy squared plus 2ad equation graphic

↓

V_fy² = V_iy² + 2ad = 0² + 2(+9.8 m/s²)(45 m) = 19.6(45)

V_fy = 30 m/s

Only X Equation

** d_x = V_xt ** (from V_x = d_x/t)

d_x - Horizontal distance
V_x - horizontal velocity

Ex 1c

Given

Same rock, thrown horizontally from the top of a cliff @ 150 m/s.
c) What was the rock's horizontal displacement (d_x, a.k.a. Range) after 3.0 seconds?

Horizontal	Vertical
V_x = 150 m/s	V_iy = 0 (thrown horizontally)
t = 3.0 sec	a_y = 9.8 m/s²
d_x = ?	d_y = 45 m
	t = 3.0 sec

↓

** d_x = V_xt ** → d_x = 150 m/s (3.0 seconds)

d_x = 450 m

Projectile Fired Horizontally →