Missile, and an aircraft.

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prostoman1

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A plane is flying in circle, with radius of 1000 km. Plane has speed of 500 km/h. The missile is fired from the center of the circle, going straight at the airplane. The missile has speed of 700 km/h. How long will it take, for the missile, to take down the aircraft?
 
Are you SURE this is an algebra problem? How might one go about it? Give us something to go on.
 
You didn't answer the second question. Please familiarize yourself with forum guidelines: https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

One can normally tell if this is an algebra problem by observing the source of the problem statement. Where did you get it? Are you taking a registered course? What course is that? Are you reading a book? What book? Why are you interested in this problem? Give us something to go on.

Can you please take a shot at describing the path of the missile? If one fires directly at the aircraft and continues on that course, will the aircraft be in the same place when the missile arrives at the aircraft's PATH?
 
I would start by writing some kind of equations to represent the airplane's circular motion: x= 1000cos(500 t), y= 1000 sin(500 t) where t is the time in hours. The missile's path is harder. The problem says the missile is "going straight at the airplane". My first thought was that the missile was aimed at the airplane and then went in a straight line in that direction- but then, since the airplane is moving, it would miss the airplane! That must mean, instead, that the missile is always changing its direction so t is constantly aiming at the current position of the airplane.

That means that the tangent line to the path is in the direction of the airplane: \(\displaystyle \frac{dy}{dx}= \frac{cos(500 t)}{sin(500 t)}\). Solve that differential equation with initial condition y(0)= 0.
 
prostoman1 said:
A plane is flying in circle, with radius of 1000 km. Plane has speed of 500 km/h. The missile is fired from the center of the circle, going straight at the airplane. The missile has speed of 700 km/h. How long will it take, for the missile, to take down the aircraft?
Click to expand...
For the missile to reach the circle that the aircraft is in [math]R = vt \implies t = \dfrac{R}{t} = \dfrac{1000 \text{ km} }{ 700 \text{ km/h} } = 1.429 \text{ h}[/math]. In order to intercept the plane the plane has to be back in its original position, so it has to have made an integer number of revolutions.

So where is the plane at 1.429 hours?

-Dan

Addendum: That is one heck of a missile to be able to fly for an hour and a half!
 
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