Thread: Microlight Prob

Ok, so im having a slight problem with getting to the same resultant as suggested by my book. Perhaps you could help me...

The microlights cruising speed in still air is 45 ms^-1, pointing in the direction of N 54◦ W but flies in a wind speed of 15.2 ms^-1 from a S 28◦ W. We Take i to be 1 ms^-1 due east and j to be 1 ms^-1 due north.
Vm - Velocity Microlight
Vw - Velocity Wind

So Vm has a magnitude of 45 and direction 28◦
The wind comes from S 28◦ W & hence blows towards N 28◦ E for which the direction is -(90◦ -28◦) hence vector Vm has a magnitude 15.2 and direction -62

The components are therefore

Vm = 45 cos(28◦)i + 45sin(28◦)
= 39.7326i + 21.1262J

Vw = 15.2 cos(-62◦)i + 15.2cos (-62)J
=-7.1360i + (-13.4208)J

so i make the resultant

v = Vm + Vw =

39.7326 + (-7.1360)i + 21.1262 + (-13.4208)J

=32.5966i & 7.7054

The suggested resultant is -29.2698i + 39.8711J, so where am i going wrong, thanks guys!

Hello, ADY!

The microlight's cruising speed in still air is 45 m/s in the direction of N54°W.
but flies in a wind speed of 15.2 m/s from S28°W.

Find its resultant vector.

The plane's vector has a magnitude of 45 and an angle of 144°.

. .


The wind's vector has a magnitude of 15.2 and an angle of 62°.

. .


The resultant vector is:

. .

. . . . . . .

Hello ADY

Originally Posted by ADY

Ok, so im having a slight problem with getting to the same resultant as suggested by my book. Perhaps you could help me...

The microlights cruising speed in still air is 45 ms^-1, pointing in the direction of N 54◦ W but flies in a wind speed of 15.2 ms^-1 from a S 28◦ W. We Take i to be 1 ms^-1 due east and j to be 1 ms^-1 due north.
Vm - Velocity Microlight
Vw - Velocity Wind

So Vm has a magnitude of 45 and direction 28◦
The wind comes from S 28◦ W & hence blows towards N 28◦ E for which the direction is -(90◦ -28◦) hence vector Vm has a magnitude 15.2 and direction -62

The components are therefore

Vm = 45 cos(28◦)i + 45sin(28◦)
= 39.7326i + 21.1262J

Vw = 15.2 cos(-62◦)i + 15.2cos (-62)J
=-7.1360i + (-13.4208)J

so i make the resultant

v = Vm + Vw =

39.7326 + (-7.1360)i + 21.1262 + (-13.4208)J

=32.5966i & 7.7054

The suggested resultant is -29.2698i + 39.8711J, so where am i going wrong, thanks guys!

Thanks for showing us all your working, but I'm afraid I don't understand how you arrived at the angles you used in your calculations. is in a direction N W, so its components are:

East and North

So:

And the wind (as you said) blows in a direction N E, so its components are:

East and North

So:

which gives a resultant velocity of:

agreeing with the answer in the book.

Grandad

Originally Posted by Soroban

Hello, ADY!


The plane's vector has a magnitude of 45 and an angle of 144°.

. .

Thank you - so i was nearly there, all apart from the angle, so how is this derived?

Thanks

Hello, ADY!

The angle of a vector is always measured from the positive -axis.
(Counter-clockwise: positive angle. .Clockwise: negative angle.)


The plane's direction is N54°W

Code:

                |
        *       |
          *     |
            *54°|
              * |
      - - - - - * - - - - -
                |

Measured from the positive x-axis, the angle is 144°.

Code:

        *
          *
            *   144°
              *
      - - - - - * - - - - -
                |

The wind's direction is from S28°W.

Code:

                |
                |
      - - - - - + - - - - -
               /|
              / |
             /  |
            /28°|
           /    |
                |

Measured from the positive x-axis, the angle is 62°.

Code:

                |    /
                |28°/
                |  /
                | /
                |/ 62°
      - - - - - + - - - - -
               /|
              / |
             /  |
            /28°|
           /    |
                |