Projectile Fired Horizontally

← Object Propelled Horizontally All Lessons Projectile, Angle →

Do Now: Define the geometry term “plane” and explain why a table top is an example of a plane surface.

Fill in the Blank Notes

Motion in a Plane

Plane — a 2-dimensional surface

Question

What kinds of objects have 2-dimensional motion?

Objects Moving Along the Earth’s Surface

Planets around Sun

The Copernican system of planetary rotation

Pendulums

Projectiles

Human Cannonball

at the 2007 State Fair of Texas

Human_Cannon_Ball.mov

Review

Object Projected Horizontally

Object propelled horizontally, dropped photo sequence

Question

1. V_iy = ?

↓

V_iy = 0

Question

2. a_y = ?

↓

a_y = 9.8 m/s²

Question

3. Horizontal Velocity?
(no air friction)

↓

Horizontal Velocity is Constant (no air friction)

V_ix = V_x = Constant

Horizontal Distance Traveled (Memorize)

d_x = V_xt

Compare Four Projectiles

4 objects thrown horizontally, same height, at various speeds

Compare their…

V_iy? • a_y? • V_y? • height (d_y)? • time spent in air?

↓

V_iy? — Same (V_iy = 0)

a_y? — Same (a_y = 9.8 m/s²)

V_y? — Same for all

height (d_y)? — Same at all times

Time spent in air — Same

Ranking Task

All objects below are thrown horizontally.

Rank the time each spends in the air from longest to shortest.

June 1997 #64

↓

Object is thrown horizontally — only height determines the time in air.

Ex 1

Given

A baseball is thrown horizontally from a grandstand 20 m above the ground at a speed of 10 m/s.
Find: (a) How long will the ball remain in flight before reaching the ground?

Horizontal Info	Vertical Info
V_x = 10 m/s	V_iy = 0 (thrown horizontally)
	a_y = +9.8 m/s²
	d_y = 20 m
	t = ?

↓

Step 3 — Substitute and Solve

d_y = V_iyt + ½a_yt²

20 m = 0 + ½(9.8 m/s²)t²

t = 2 seconds

Ex 1 (b)

Given

Same baseball (V_x = 10 m/s, t = 2 sec, from part (a)).
Find: What is the projectile’s maximum range before it hits the ground?

Range (d_x)

Horizontal	Vertical
V_x = 10 m/s	V_iy = 0 (thrown horizontally)
d_x = ?	a_y = +9.8 m/s²
t = 2 sec	d_y = 20 m
	t = 2 sec

↓

Horizontal Displacement (d_x)

d_x = V_xt

= (10 m/s)(2 sec)

= 20 m

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Review

Question

Which velocity is constant for all spheres?

↓

V_x

AP Question

Hewitt Question

Given

A cannonball is fired horizontally at 10 m/s from a cliff. Its speed one second after being fired is about:
A. 10 m/s B. 14 m/s C. 16 m/s D. 20 m/s

↓

V_x = V_y
= 10 m/s

V = 14 m/s

AP Physics

Review of Freefall

Question

Compare the time it takes for a whiffle ball to go up with the time it takes to reach its initial position.

↓

Takes longer to return from the peak — friction causes the average velocity to be less on the way down.

Ex 2

Given

A baseball is dropped from the top of bleachers at a height of 80. meters. At the same time, another ball is thrown horizontally. Both balls hit level ground 50. m apart. (Air resistance is negligible.)
Find: the horizontal velocity of the thrown ball.

↓

Time in Air

Δd_y = V_iyt + ½a_yt²

Δd_y = ½a_yt²

80 m = (4.9 m/s²)t²

t = 4 sec

V_x = d_x/t
= 50 m / 4 sec

V_x = 13 m/s

Ex 3

Given

An object moving horizontally with speed V falls off the edge of a vertical cliff and lands a distance d from the base of the cliff.
Find: How far from the base of the cliff would the object land if the height of the cliff was doubled?

↓

d_x = V_xt
= d

d_y = ½at²

Double d_y, then t increases by √2

(√2)d, or 1.4d

Ex 4

Given

From a cliff of height 28.8 m above the ground, a ball is thrown horizontally with an initial velocity of 7.0 m/s.
Find: What is the range of the ball?

↓

d_x = V_xt

Δd_y = ½a_yt²

28.8 m = 4.9t²

t = 2.4 sec

d_x = V_xt
= (7.0 m/s)(2.4 s)

d_x = 17 m

Frame of Reference

http://www.archive.org/

Producer: Richard Leacock. Production Company: Educational Development Corp. Sponsor: Eric Prestamon. Audio/Visual: sound, black and white. PSSC

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. Four balls are thrown horizontally from the same height at different speeds. Ignoring air, how do their times in the air compare?

2. A ball is thrown horizontally at 10 m/s from 19.6 m high. What is its range? (g = 9.8 m/s²)

3. A cannonball is fired horizontally at 10 m/s from a cliff. About what is its speed 1 s later? (g ≈ 10 m/s²)

4. An object rolls off a cliff and lands a distance d from the base. If the cliff were twice as high, how far would it land?

5. For a ball thrown horizontally with no air friction, which quantity stays constant?

Projectile, Angle →