It is often helpful to draw a diagram of the problem, with important values labeled. Although almost every problem is stated using an illustration,
we sometimes find it useful to draw an additional diagram.
Variables
We summarize the variables relating to the problem in a table. Some of these have values given in the problem statement or illustration. If we
do not know the value of a variable, we enter the variable symbol. A variable table for the problem stated above is shown.There are two reasons we write the variables. One is so that if you see a variable with which you are unfamiliar, you can quickly see what it
represents. The other is that it is another useful problem-solving technique: Write down everything you know. Sometimes you know more than
you think you know! Some variables may also prompt you to think of ways to solve the problem.After these two steps, we move to strategy.
What is the strategy?
The strategy is a summary of the sequence of steps we will follow in solving the problem. Some students who used this book early in its
development called the strategy section “the hints,” which is another way to think of the strategy. There are typically many ways to solve a
problem; our strategy is the one we chose to employ. (As we point out in the text when we actually solve this problem, there is another efficient
manner in which to solve it.)
For the problem above, our strategy was:- There are two unknowns, the initial and final velocities, so choose two equations that include these two unknowns and the values you
do know. - Substitute known values and use algebra to reduce the two equations to one equation with a single unknown value.
Principles and equations
Principles and equations from physics and mathematics are often used to solve a problem. For the problem above, for example, these two
linear motion equations that apply when acceleration is constant are useful:
vf = vi + at
ǻx = ½(vi + vf)t
The physics principles are the crucial points that the problems are attempting to reinforce. If they look quite familiar to you at some point: Great!
Step-by-step solution
We solve the problem (or work through the derivation) in a series of steps. We provide a reason for each step. If you want a more detailed
explanation, you can click on a step, which causes a more detailed text explanation to appear on the right. Some students find the additional
information quite helpful; others prefer the very brief explanation. It also varies depending on the difficulty of the problem í everyone can use a
little help sometimes.
Here are the first three steps that we used to solve the problem above.displacement ǻx = 11.8 m
acceleration a = 1.21 m/s^2
elapsed time t = 3.14 s
initial velocity vi
final velocity vf
Step Reason
1. vf = vi + at first motion equation
2. vf = vi + (1.21 m/s^2 ) (3.14 s) substitute values
3. vf = vi + 3.80 m/s multiply
0.4 - Interactive checkpoints
The great pyramid of Cheops has a
square base with edges that are
almost exactly 230 m long. The side
faces of the pyramid make an angle
of 51.8° with the ground.
The apex of the pyramid is directly
above the center of the base. Find its
height.
(^4) Copyright 2000-2007 Kinetic Books Co. Chapter 00