A person moves towards north a distance 20m from point P and reaches at Q. He turns 135 degrees in clockwise direction and goes 40√2m. 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 ..??..🤨🤨
Anyone plz explain 🙏🙏📒📕📖📐📐
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..🤔🤔🤨🤨😐😕
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 40√2m 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) * 40√2
- Vertical component: sin(135) * 40√2
cos(135) = -sqrt(2)/2
sin(135) = sqrt(2)/2
- Horizontal component: -sqrt(2)/2 * 40√2 = -40
- Vertical component: sqrt(2)/2 * 40√2 = 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 ≈ 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