IIT-JEE 2011 - Career Point

Translated into symbols, this becomes "What is
the value of x when v x = 25 m/s?"
Make a list of quantities such as x, x 0 ,v x ,v 0x ,a x and
t. In general, some of the them will be known
quantities, and decide which of the unknowns are
the target variables. Be on the lookout for implicit
information. For example. "A are sits at a
stoplight" Usually means v 0x = 0.
Step 3 : Execute the solution :
Choose an equation from Equation v x = v 0x + a x t
x = x 0 + v 0x t + 2
1
ax t 2
2
v x =
(constant acceleration only)
2
v 0x
+ 2a x (x – x 0 ) (constant accelerations only)
⎛ v0x
+ vx
⎞
x – x 0 = ⎜ ⎟ t (constant acceleration only)
⎝ 2 ⎠
that contains only one of the target variables. Solve
this equation for the equation for the target variable,
using symbols only. then substitute the known values
and compute the value of the target variable.
sometimes you will have to solve two simultaneous
equations for two unknown quantities.
Step 4 : Evaluate your answer : Take a herd look at
your results to see whether they make sense. Are
they within the general range of values you
expected?
Problem solving strategy :
Projectile Motion :
Step 1 : Identify the relevant concepts : The key
concept to remember is the throughout projectile
motion, the acceleration is downward and has a
constant magnitude g. Be on the lookout for aspects
of the problem that do not involve projectile motion.
For example, the projectile-motion equations don't
apply to throwing a ball, because during the throw
the ball is acted on by both the thrower's hand and
gravity. These equations come into play only after
the ball leaves the thrower's hand.
Step 2 : Set up the problem using the following steps
Define your coordinate system and make a sketch
showing axes. Usually it's easiest to place the
origin to place the origin at the initial (t = 0)
position of the projectile. (If the projectile is a
thrown ball or a dart shot from a gun, the
thrower's hand or exits the muzzle of the gun.)
Also, it's usually best to take the x-axis as being
horizontal and the y-axis as being upward. Then
the initial position is x 0 = 0 and y 0 = 0, and the
components of the (constant) acceleration are a x = 0,
a y = – g.
List the unknown and known quantities, and
decide which unknowns are your target variables.
In some problems you'll be given the initial
velocity (either in terms of components or in
terms of magnitude and direction) and asked to
find the coordinates and velocity components as
some later time. In other problems you might be
given two points on the trajectory and asked to
find the initial velocity. In any case, you'll be
using equations
x = (v 0 cosα 0 )t (projectile motion) through ...(1)
v y = v 0 sin α 0 – gt (projectile motion) ...(2)
make sure that you have as many equations as
there are target variables to be found.
It often helps to state the problem in words and
then translate those words into symbols. For
example, when does the particle arrive at a certain
point ? (That is at what value of t?) Where is the
particle when its velocity has a certain value?
(That is, what are the values of x and y when v x or
v y has the specified value ?) At the highest point
in a trajectory, v y = 0. so the question "When does
the particle reach its highest points ?" translates
into "When does the projectile return to its initial
elevation?" translates into "What is the value of t
when y = y 0 ?"
Step 3 : Execute the solution use equation (1) & (2)
to find the target variables. As you do so, resist the
temptation to break the trajectory into segments and
analyze each segment separately. You don't have to
start all over, with a new axis and a new time scale,
when the projectile reaches its highest point ! It's
almost always easier to set up equation (1) & (2)
at the starts and continue to use the same axes and
time scale throughout the problem.
Step 4 : Evaluate your answer : As always, look at
your results to see whether they make sense and
whether the numerical values seem reasonable.
Relative Velocity :
Step 1 : Identify the relevant concepts : Whenever
you see the phrase "velocity relative to" or "velocity
with respect to", it's likely that the concepts of
relative will be helpful.
Step 2 : Set up the problem : Label each frame of
reference in the problem. Each moving object has its
own frame of reference; in addition, you'll almost
always have to include the frame of reference of the
earth's surface. (Statements such as "The car is
traveling north at 90 km/h" implicitly refer to the
car's velocity relative to the surface of the earth.) Use
the labels to help identify the target variable. For
example, if you want to find the velocity of a car (C)
with respect to a bus (B), your target variable is v C/B .
Step 3 : Execute the solution : Solve for the target
variable using equation
v P/A = v P/B + v B/A (relative velocity along a line) ...(1)
XtraEdge for IIT-JEE 30 MAY 2010