The point of no return for plane making round trip from fld.

[hungrybarts]

I really like geometry but this exercise is really frustrating. I have spent hours doing this but I'm still stuck :?:
So, I would like some help to solve this step by step. Thanks

 

[Deleted member 4993]

Re: The point of no return

First of all, I couldn't read right side of the problem. It is a good idea to review what you have posted - after you have posted - and then correct it.

This is an easy problem - does not need geometry - need some algebra and the knowledge of following equation:

distance of travel = speed of travel * time of travel

For the fist part - assume

distance of travel = d + d = 2*d (why?)

time to travel with the wind t = d/(300 + 50)(why?)......................................(1)

or

d = t * (300 + 50)

d/t = 300 + 50 .......................................................(2)

time to travel against the wind (4 - t) = d/(300 - 50) (why?)...........................(3)

then,

d = (4 - t) * (300 - 50)

d/(4-t) = 300 - 50 ................................................(4)

adding (2) and (4) you get

d = 600 * t * (4-t).........................................................(5)

adding (1) and (3) you get

4 = d/350 + d/250.......................................................(6)

Solve for 'd' from above (6).

Now about the graph.

What is the relationship between between 'time' and 'distance' (look at the equation above)?

How does the 'slope' of the line change with 'speed' ?

If you are still stuck, write back showing your work/thoughts.

 

[stapel]

I really like geometry but this exercise is really frustrating. I have spent hours doing this but I'm still stuck....

In future, kindly show your work. (If you've been "hours doing this", then you should have much you could have displayed.) Also, please type out textual information (it hardly seems fair to require others first to figure out what your question is) and provide a detailed description of any required graphics (which, for some reason, you did not include in your picture).

Thank you for your consideration.

Imagine that you are a pilot of the light aircraft in the picture [omitted], which is capable of cruising at a steady speed of 300 kph in still air. You have enough fuel on board to last four hours.

You take off from the airfield and on the outward journey are helped along by a 50 kph wind which increases your cruising speed relative to the ground to 350 kph. Suddenly you realize that on your return journey you will be flying into the wind and will therefore slow down to 250 kph.

What is the maximum distance that you can travel from the airfield and still be sure that you have enough fuel to make a safe return journey? Investigate these "points of no return" for different wind speeds.

SOME HINTS:
1. Draw a graph to show how your distance from the airfield will vary with time.
. . .a) How can you show an outward speed of 350 kph?
. . .b) How can you show a return speed of 250 kph?
2. Use your graph to find the maximum distance you can travel from the airfield, and the time at which you should return.
3. On the same graph, investigate the "points of no return" for different wind speeds. What kind of pattern do these points make?
4. Suppose the wind speed is "w" kph and the "point of no return" is "d" km from the airfield and the time at which you should turn around is "t" hours.
. . .a) Write down an expression for the outward speed of the aircraft involving w, d, and t.
. . .b) Write down an expression for the homeward speed of the aircraft involving w, d, and t.
. . .c) Try to express d only in terms of t, eliminating w from the two resulting equations.
. . .d) Does this explain the pattern made by your "points of no return"?

Please reply with a clear listing of your work and reasoning so far, showing the progress you have made in following the provided "hints" and the explanation provided earlier by the tutor.

Please be complete. Thank you.

Eliz.

 

[hungrybarts]

Re: The point of no return

allrighto here is my working and i suppose it has covered 1-3
now all i need to do is 4 :idea:

 

[Deleted member 4993]

Re: The point of no return

Look at my solution carefully - I have given you hints about #4.