# Thread: resultant velocity

1. ## resultant velocity

A plane is flying $\displaystyle E40^oN$ at a speed of $\displaystyle 600km/h$. The wind is blowing at $\displaystyle 10km/h$ in the direction $\displaystyle N20^oW$. Determine the resultant velocity of the plane.

i got $\displaystyle 601.81 km/h$ and $\displaystyle 0.93^o$

correct?

2. I've got 603.49 km/h and bearing $\displaystyle 049.1^o$

What I did was:

$\displaystyle Resultant = \sqrt{10^2 + 600^2 - 2(600)(10)cos(110)}$

3. Hello, euclid2!

I got different answers . . .

$\displaystyle \text{A plane is flying }E40^oN\text{ at a speed of 600 km/h}$.
$\displaystyle \text{The wind is blowing at 10 km/h in the direction }N20^oW$
$\displaystyle \text{Determine the resultant velocity of the plane.}$

$\displaystyle \text{i got: 601.81 km/h and }0.93^o$

In the diagram, "d" represents "degrees".

Code:
                     C
o           Q
*  *  10     :
*     *       :
*        *     :
*           *20d:
P         *          70d * :
:        *    W - - - - - -o B
:       *           40d *
:      *             *
:     *           *
:    *         * 600
:   *       *
:  *     *
: *   *
:* * 40d
A o - - - - - - - - - - - E

The plane starts at $\displaystyle \,A$ and flies to $\displaystyle \,B.$
. . $\displaystyle \angle BAE \,=\, 40^o \,=\,\angle W\!BA$
. . $\displaystyle AB \,=\,600$

The wind blows from $\displaystyle \,B$ to $\displaystyle \,C,$
. . $\displaystyle BC \,=\,10$
. . $\displaystyle \angle CBQ \,=\,20^o \quad\Rightarrow\quad \angle CBW = 70^o$

In $\displaystyle \Delta ABC\!:\;\;AB = 600,\;BC = 10,\;\angle ABC = 110^o$

Law of Cosines: .$\displaystyle AC^2 \:=\:600^2 + 10^2 - 2(600)(10)\cos110^o \:=\:364,\!204.2417$

Therefore: .$\displaystyle AC \:=\:603.4933651 \quad\Rightarrow\quad \boxed{AC \:\approx\:603.5}$

$\displaystyle \cos(\angle C\!AB) \;=\;\dfrac{600^2 + 603.5^2 - 10^2}{2(600)(603.5)} \;=\;0.999878832$

Hence: .$\displaystyle \angle C\!AB \;=\;0.891941392^o \;\approx\;0.89^o$

Then: .$\displaystyle \angle P\!AC \;=\;90^o - 0.89^o - 40^o \;=\;49.11^o$

Therefore, the heading of the plane is: .$\displaystyle N49.11^oE$

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# what is formula of resultant velocity

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