Computing Wind Speed The average airspeed of a singleengine aircraft is 150 miles per hour. If t

Computing Wind Speed The average airspeed of a singleengine...

Key Concepts

Relative Speed

This concept involves understanding how an object's speed is affected by an external moving medium, such as wind or current. The effective speed of the object, when moving with or against the external force, is adjusted by adding or subtracting the speed of the medium. This is critical in problems involving wind speed because it determines the actual speed of the aircraft relative to the ground.

Time-Distance-Speed Relationship

This fundamental relationship in kinematics states that distance equals speed multiplied by time. It is used to set up equations that describe the motion of an object under different conditions, such as with and against the wind. In problems like these, comparing the distances covered over different time periods under varying effective speeds allows for the creation of equations that can be solved for the unknown variable, in this case, the wind speed.

System of Equations

When a problem involves multiple scenarios or conditions that lead to different expressions for the same physical quantity (like distance), a system of equations can be established. Each scenario provides an equation that relates the known and unknown values. Solving this system enables one to isolate and compute the unknown variable, such as the wind speed affecting an aircraft's effective speed.

Transcript

00:02 The problem we're about to work involves a real -life scenario with which we will use a system of linear equations to solve.

00:12 In fact, this problem is going to require that we set up a system of two linear equations and two variables.

00:21 Now, there's many different ways, several different ways, to solve such a system of equations.

00:27 After we set up the equations, the system in this problem, i will just, with you the method that i choose to work with it and i'll go over with you why i chose that method.

00:38 Okay, so let's get started with this problem.

00:41 Okay, this problem involves the average speed of an aircraft is 150 miles per hour and that the distance travel with the wind takes two hours.

01:10 There's a certain distance travel with the wind that it takes two hours to make that trip and then the same distance against the wind takes three hours.

01:31 Now we're asked to find what the wind speed is.

01:37 So on this problem there is a formula that we will walk with, a very well -known formula that you've all worked with many times, and that is that distance traveled is equal to the time traveled times the rate at which he traveled.

02:05 So in working with this problem, as with any application problem, one of the first things you want to do is state what your variables are and what they represent and then use those variables and the information in the problem to write some equations.

02:24 So on this problem, i'm going to let d stand for distance traveled and i'm going to let w represent the wind speed.

02:45 Now keep in mind that the question wanted us to find the wind speed.

02:56 Okay so i'm going to use the information in the problem along with the variables i just represented and try to come up with an equation.

03:06 It tells us that the average speed of this aircraft is 150 miles per hour so we know the rate of the aircraft.

03:16 Okay we also told the distance when you're going with the wind takes two hours.

03:23 So i'm going to set up an equation using this formula that i had already put up here about distance and i'm going to say d equals two hours times the rate of the aircraft plus the little extra push that that wind gives it.

03:46 If you're going with the wind, the wind is going to increase your speed.

03:51 So i take the speed of the aircraft as if it will instill air, no wind affecting it, and add to it the speed of the wind.

04:02 Okay, there's my first equation...

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