Step-by-step solution

In step 4, we take the square root of 106 to find the final velocity. We chose the positive square root, since the runner is moving in the positive

direction. When there are multiple roots, you look at the problem to determine the solution that makes sense given the circumstances. If the

runner were running to the left, then a negative velocity would be the appropriate choice.

Step Reason

1. vf

(^2) = v
i
(^2) + 2aǻx

motion equation

2. enter known values

3. vf^2 = 106 m^2 /s^2 multiplication and addition

4. vf = 10.3 m/s take square root

2.17 - Interactive checkpoint: passenger jet

A passenger jet lands on a runway

with a velocity of 71.5 m/s. Once it

touches down, it accelerates at a

constant rate of í3.17 m/s^2.

How far does the plane travel down

the runway before its velocity is

decreased to 2.00 m/s, its taxi speed

to the landing gate?

Answer:

ǻx = m

2.18 - Free-fall acceleration

Free-fall acceleration: Rate of acceleration due

to the force of Earth's gravity.

Galileo Galilei is reputed to have conducted an interesting experiment several hundred

years ago. According to legend, he dropped two balls with different masses off the

Leaning Tower of Pisa and found that both landed at the same time. Their differing

masses did not change the time it took them to fall. (We say he was “reputed to have”

because there is little evidence that he in fact conducted this experiment. He was more

of a “roll balls down a plane” experimenter.)

Today this experiment is used to demonstrate that free-fall acceleration is constant: that

the acceleration of a falling object due solely to the force of gravity is constant,

regardless of the object’s mass or density. The two balls landed at the same time

because they started with the same initial velocity, traveled the same distance and

accelerated at the same rate. In 1971, the commander of Apollo 15 conducted a version

of the experiment on the Moon, and demonstrated that in the absence of air resistance,

a hammer and a feather accelerated at the same rate and reached the surface at the

same moment.

In Concept 1, you see a photograph that illustrates free-fall acceleration. Pictures of a

freely falling egg were taken every 2/15 of a second. Since the egg’s speed constantly

increases, the distance between the images increases over time. Greater displacement

over the same interval of time means its velocity is increasing in magnitude; it is

accelerating.

Free-fall acceleration is the acceleration caused by the force of the Earth’s gravity,

ignoring other factors like air resistance. It is sometimes stated as the rate of

acceleration in a vacuum, where there is no air resistance. Near the Earth’s surface, its

magnitude is 9.80 meters per second squared. The letter g represents this value. The

value of g varies slightly based on location. It is less at the Earth's poles than at the

equator, and is also less atop a tall mountain than at sea level.

Free-fall acceleration

Acceleration due to gravity

Galileo's famous experiment

Confirmed by Apollo 15 on the Moon

(^40) Copyright 2000-2007 Kinetic Books Co. Chapter 02