#2
A spy stands on the sidewalk by an apartment building examining a foreign embassy across the street. The spy then climbs 30 m to the top the building and then slides 40 m along a wire at a 20° angle below right to reach a window on the embassy. What is their total displacement from the sidewalk to the embassy window? (I'm not too sure which way the 20 degree wire is going)
The x- components : 40 cos 20= 37.588
The y- components : 30-40 sin 20= -6.518
Resultant: <37.588, -6.518>
Final answer is 38.149
#3
An army tank division leaves base and travels 30 miles at 30° S of W and then turns and travels 70 miles at 10° N of W. What is their total displacement from base at the end of the trip?
A= <30 cos 210, 30 sin 210>
B= <70 cos 170, 70 sin 170>
Resultant: <-94.917, -2.845>
Final answer is 94.959 m
#4
A spider starts walking from the center of a piece of paper and walks 10 cm at 15° N of W and then walks 23 cm at 70° S of E before resting. What is the spider’s total displacement from the center to their resting place?
A= <10 cos 165, 10 sin 165>
B = <23 cos 290, 23 sin 290>
Resultant: <-1.793, -19.025>
Final answer is 19.109 cm
#5
A hiker starts at the base of the trail and hikes 350 m up a slope at a 10° angle above right. They come to a switchback and head 500 m up a slope at 7° above left. What is the hiker’s total displacement from the base of the trail when they reach the end of the second leg?
A= <350 cos 10, 350 sin 10>
B= <500 cos 173, 500 sin 173>
Resultant: <-151.590, 121.712>
Final answer is 194.405 m
***I reposted this questions becuase they weren't answered.
#2: 30-40 sin 20 = 16.31
#3: ok
#4: ok
#5: ok
thx Steve, appreciate you help
I apologize for the oversight. Let me answer these questions for you.
#2
To find the total displacement, we need to break down the movements into their x and y components.
- The spy climbs 30 m vertically, so the y-component is 30.
- The spy then slides 40 m at a 20° angle below the horizontal, so the x-component is 40 * cos(20°) ≈ 37.588 and the y-component is -40 * sin(20°) ≈ -13.036.
The resultant displacement from the sidewalk to the embassy window is the vector sum of the x and y components:
Resultant = <37.588, 30 - 13.036> = <37.588, 16.964>.
The magnitude of this vector is the length or displacement:
|Resultant| = sqrt((37.588)^2 + (16.964)^2) ≈ 41.17.
Therefore, the total displacement from the sidewalk to the embassy window is approximately 41.17 meters.
#3
To find the total displacement, we need to break down the movements into their x and y components.
- The tank division travels 30 miles at a direction 30° south of west.
- The x-component is 30 * cos(210°) ≈ -25.980
- The y-component is 30 * sin(210°) ≈ -15.
- The tank division then turns and travels 70 miles at a direction 10° north of west.
- The x-component is 70 * cos(170°) ≈ -67.851
- The y-component is 70 * sin(170°) ≈ -11.617
The resultant displacement from the base is the vector sum of the x and y components:
Resultant = <-25.980 - 67.851, -15 - 11.617> = <-93.831, -26.617>.
The magnitude of this vector is the length or displacement:
|Resultant| = sqrt((-93.831)^2 + (-26.617)^2) ≈ 97.373.
Therefore, the total displacement from the base at the end of the trip is approximately 97.373 miles.
#4
To find the total displacement, we need to break down the movements into their x and y components.
- The spider walks 10 cm at a direction 15° north of west.
- The x-component is 10 * cos(165°) ≈ -8.660
- The y-component is 10 * sin(165°) ≈ 2.588
- The spider then walks 23 cm at a direction 70° south of east.
- The x-component is 23 * cos(290°) ≈ -13.004
- The y-component is 23 * sin(290°) ≈ -19.874
The resultant displacement from the center to the resting place is the vector sum of the x and y components:
Resultant = <-8.660 - 13.004, 2.588 - 19.874> = <-21.664, -17.286>.
The magnitude of this vector is the length or displacement:
|Resultant| = sqrt((-21.664)^2 + (-17.286)^2) ≈ 27.689.
Therefore, the spider's total displacement from the center to their resting place is approximately 27.689 cm.
#5
To find the total displacement, we need to break down the movements into their x and y components.
- The hiker hikes 350 m at a direction 10° above the horizontal.
- The x-component is 350 * cos(10°) ≈ 340.278
- The y-component is 350 * sin(10°) ≈ 60.739
- The hiker then hikes 500 m at a direction 7° above the opposite horizontal.
- The x-component is 500 * cos(173°) ≈ -480.970
- The y-component is 500 * sin(173°) ≈ -97.734
The resultant displacement from the base when they reach the end of the second leg is the vector sum of the x and y components:
Resultant = <340.278 - 480.970, 60.739 - 97.734> = <-140.692, -36.995>.
The magnitude of this vector is the length or displacement:
|Resultant| = sqrt((-140.692)^2 + (-36.995)^2) ≈ 146.726.
Therefore, the hiker's total displacement from the base of the trail when they reach the end of the second leg is approximately 146.726 m.