Author Topic: Vectors (Read 578 times) Tweet Share

darkphoenix · « **on:** June 14, 2010, 10:57:25 pm »

A person walks for 2km in a direction of N 15degrees E, then turns right through 90degrees to the original direction. The person then walks for a further distance of 1km. Find the magnitude of the resultant displacement and the angle between this vector and the person's original direction.

Someone help me?

m@tty · « **Reply #1 on:** June 15, 2010, 12:33:41 am »

After the initial 2km walk the person is $2\cos(15) km$ north of the starting point and $2\sin(15) km$ east.

After turning they are travelling S 75^o E and they go 1km, so a further $\sin(75) km$ east and $\cos(75) km$ south.

Total displacement north = $2\cos(15)-\cos(75)\approx 1.673 km$

Displacement east = $2\sin(15)+\sin(75)\approx 1.484$

Displacement = $\sqrt{(2\cos(15)-\cos(75))^2+(2\sin(15)+\sin(75))^2}$ .

At an angle of $\arctan\left(\frac{1.484}{1.673}\right)$ to the vertical.

So it makes an angle of $\arctan\left(\frac{1.484}{1.673}\right)-15$ to the original direction.

EDIT: The final calculations of angle must be in degrees of course.

darkphoenix · « **Reply #2 on:** June 15, 2010, 11:19:15 pm »

hoping for an earlier response but thanks anyway man.

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Author Topic: Vectors (Read 578 times) Tweet Share

darkphoenix

Vectors

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