May 2011 - Career Point

Translated into symbols, this becomes "What isthe 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 andt. In general, some of the them will be knownquantities, and decide which of the unknowns arethe target variables. Be on the lookout for implicitinformation. For example. "A are sits at astoplight" Usually means v 0x = 0.Step 3 : Execute the solution :Choose an equation from Equation v x = v 0x + a x tx = x 0 + v 0x t + 21ax t 22v x =(constant acceleration only)2v 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. Solvethis equation for the equation for the target variable,using symbols only. then substitute the known valuesand compute the value of the target variable.sometimes you will have to solve two simultaneousequations for two unknown quantities.Step 4 : Evaluate your answer : Take a herd look atyour results to see whether they make sense. Arethey within the general range of values youexpected?Problem solving strategy :Projectile Motion :Step 1 : Identify the relevant concepts : The keyconcept to remember is the throughout projectilemotion, the acceleration is downward and has aconstant magnitude g. Be on the lookout for aspectsof the problem that do not involve projectile motion.For example, the projectile-motion equations don'tapply to throwing a ball, because during the throwthe ball is acted on by both the thrower's hand andgravity. These equations come into play only afterthe ball leaves the thrower's hand.Step 2 : Set up the problem using the following stepsDefine your coordinate system and make a sketchshowing axes. Usually it's easiest to place theorigin to place the origin at the initial (t = 0)position of the projectile. (If the projectile is athrown ball or a dart shot from a gun, thethrower's hand or exits the muzzle of the gun.)Also, it's usually best to take the x-axis as beinghorizontal and the y-axis as being upward. Thenthe initial position is x 0 = 0 and y 0 = 0, and thecomponents of the (constant) acceleration are a x = 0,a y = – g.List the unknown and known quantities, anddecide which unknowns are your target variables.In some problems you'll be given the initialvelocity (either in terms of components or interms of magnitude and direction) and asked tofind the coordinates and velocity components assome later time. In other problems you might begiven two points on the trajectory and asked tofind the initial velocity. In any case, you'll beusing equationsx = (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 asthere are target variables to be found.It often helps to state the problem in words andthen translate those words into symbols. Forexample, when does the particle arrive at a certainpoint ? (That is at what value of t?) Where is theparticle when its velocity has a certain value?(That is, what are the values of x and y when v x orv y has the specified value ?) At the highest pointin a trajectory, v y = 0. so the question "When doesthe particle reach its highest points ?" translatesinto "When does the projectile return to its initialelevation?" translates into "What is the value of twhen y = y 0 ?"Step 3 : Execute the solution use equation (1) & (2)to find the target variables. As you do so, resist thetemptation to break the trajectory into segments andanalyze each segment separately. You don't have tostart all over, with a new axis and a new time scale,when the projectile reaches its highest point ! It'salmost always easier to set up equation (1) & (2)at the starts and continue to use the same axes andtime scale throughout the problem.Step 4 : Evaluate your answer : As always, look atyour results to see whether they make sense andwhether the numerical values seem reasonable.Relative Velocity :Step 1 : Identify the relevant concepts : Wheneveryou see the phrase "velocity relative to" or "velocitywith respect to", it's likely that the concepts ofrelative will be helpful.Step 2 : Set up the problem : Label each frame ofreference in the problem. Each moving object has itsown frame of reference; in addition, you'll almostalways have to include the frame of reference of theearth's surface. (Statements such as "The car istraveling north at 90 km/h" implicitly refer to thecar's velocity relative to the surface of the earth.) Usethe labels to help identify the target variable. Forexample, 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 targetvariable using equationv P/A = v P/B + v B/A (relative velocity along a line) ...(1)XtraEdge for IIT-JEE 27 MAY 2011