Physics help? Resultant velocity, 2m/s W etc.?

on an x,y grid

graph the two given vectors

conventionally N is +y and E is +x

so

you have 2 units left from origin on the -x axis

and 8 units up on the +y axis

now

use these as sides and construct a parallelogram

(through the tip of each given draw the parallel to the other given and note where they intersect)

draw from origin to the intersection

this is the resultant

now

find its length and direction

(notice that we have a right triangle)

length = sqrt(8^2 + 2^2) = 8.25 units

and the resultant is closer to the y axis

so

tan(angle) = 2/8 = 0.25

angle = 14.0°

finally we report the cat's velocity as

8.25 m/s, 14.0° W of N

of course, we have assumed that the cat is freely carried by the wind

much as a boat is carried by the current in a river

The cat is simultaneously moving:

2 m/w west and

8 m/s north

We have to add these 2 perpendicular vectors to find the resultant velocity, V.

The magnitude of V is given by:

||V||^2 = 2^2 + 8^2

||V|| = 8.25m/s

The direction of V is an angle A, west of north, where

tan(A) = 2/8

A = tan-1(0.25)

A = 14degrees

So the resultant velocity is 8.25m/s, 14 degrees west of north.

If you didn't follow the maths, watch the video-lesson in the link.

What is "W" here - "A mentally challenged cat named Felix run

2m/s #W# while a very strong wind pushes

him 8 m/s North."

I am answering assuming it as West side.

P = 8

Q = 2

as wind blows to west and cat goes to north, angle or @ = 90 degree

We know R = squareroot(P^2 + Q^2 + 2PQcos@)

= squareroot(8^2+ 2^2 + 2*8*2*cos90)

= squareroot(64+4+0)

= squareroot(68)

= 8.25 m/s

It's the answer.

The two velocity vectors are at right angles. They are the legs of a right triangle. The resultant vector is the hypotenuse.

Make a quick sketch to help see the relationships.

magnitude = sqrt(2^2 + 8^2)

direction = arctan (8/2) degrees north of west.