A person moves towards north a distance 20m from point P and reaches at Q. He turns 135 degrees in clockwise direction and goes 40โˆš2m. From here he turns 135 degrees clockwise and goes 25m. How far is he now from his initial position?

(If you could, could you explain with a rough illustration or something-for better understanding?)

Thanks!

I didn't get it at all ..??..๐Ÿคจ๐Ÿคจ

Anyone plz explain ๐Ÿ™๐Ÿ™๐Ÿ“’๐Ÿ“•๐Ÿ“–๐Ÿ“๐Ÿ“

A PERSON MOVES TOWARDS NORTH A DISTANCE OF 25 M FROM A POINT P AND REACHES AT Q. HE TURNS 135 DEGREE CLOCKWISE AND GOES 25*UNDERROOT 2 (i.e. root 2) M . FROM HERE HE TURNS 135 DEGREE CLOCKWISE AND GOES 20 M

Can u plz explain it..๐Ÿค”๐Ÿค”๐Ÿคจ๐Ÿคจ๐Ÿ˜๐Ÿ˜•

To solve this problem, let's break it down step by step:

Step 1: Start at point P.
Step 2: The person moves towards the north a distance of 20m and reaches point Q.
Step 3: Now, the person turns 135 degrees in the clockwise direction.

To visualize this, imagine you are facing north at point Q. Turning 135 degrees clockwise would make you face the east-southeast direction.

Step 4: The person moves 40โˆš2m in this new direction.

Now, let's calculate the displacement in the east-southeast direction. We can use trigonometry to find the horizontal and vertical components of the displacement:

- Horizontal component: cos(135) * 40โˆš2
- Vertical component: sin(135) * 40โˆš2

cos(135) = -sqrt(2)/2
sin(135) = sqrt(2)/2

- Horizontal component: -sqrt(2)/2 * 40โˆš2 = -40
- Vertical component: sqrt(2)/2 * 40โˆš2 = 40

So, the person moves -40m horizontally and 40m vertically.

Step 5: Now, the person turns another 135 degrees clockwise.

To visualize this, imagine you are facing east-southeast. Turning 135 degrees clockwise would make you face the south direction.

Step 6: The person moves 25m in this new direction.

Now, let's calculate the displacement in the south direction:

- Horizontal component: 0m (since there is no east-west displacement)
- Vertical component: -25m

Step 7: To find the final displacement, we need to add up all the horizontal and vertical components:

- Total horizontal displacement: 0m - 40m = -40m
- Total vertical displacement: 40m - 25m = 15m

Step 8: Now, we can use the Pythagorean theorem to find the distance from the initial position (point P) to the final position:

distance = sqrt((total horizontal displacement)^2 + (total vertical displacement)^2)
distance = sqrt((-40m)^2 + (15m)^2)
distance = sqrt(1600m^2 + 225m^2)
distance = sqrt(1825m^2)
distance โ‰ˆ 42.77m (rounded to two decimal places)

So, the person is approximately 42.77m away from their initial position.

I hope this explanation helps! Let me know if you have any further questions.

sorry, bud -- no illustrations here.

P is at (0,0) PQ heading is N
Q is at (0,20) QR heaing is SE
R is at (40,-20) RS heading is W
S is at (15,-20)

PS is thus 25