pls explain to me how you add
65km{North 85 degreesWest], 3500m[South 10 West}, 6000m{East 70 degrees South], 54km[North 60 degrees East].
pls explain to me how i should add these vectors. I really need help. pls help
To add these vectors, you need to break them down into their north-south and east-west components. Once you have the components, you can add them separately to get the total north-south and east-west distances.
Let's break down each vector into its components:
1. 65km[North 85 degrees West]:
- North-south component: 65km * sin(85°) = 64.065km towards the north
- East-west component: 65km * cos(85°) = -11.986km towards the west (negative because it is west)
2. 3500m[South 10 West]:
- North-south component: -3500m * sin(10°) = -605.463m towards the south (negative because it is south)
- East-west component: -3500m * cos(10°) = -3493.79m towards the west (negative because it is west)
3. 6000m[East 70 degrees South]:
- North-south component: -6000m * cos(70°) = -2741.3m towards the south (negative because it is south)
- East-west component: 6000m * sin(70°) = 5747.17m towards the east
4. 54km[North 60 degrees East]:
- North-south component: 54km * cos(60°) = 27km towards the north
- East-west component: 54km * sin(60°) = 46.8km towards the east
Now let's add the components separately:
North-south component = 64.065km - 605.463m - 2741.3m + 27km = -3446.698m = -3.446698km (since meters and kilometers have different units, we converted everything to kilometers)
East-west component = -11.986km - 3493.79m + 5747.17m + 46.8km = 137.194km
To find the magnitude and direction of the resulting vector, you can use the Pythagorean theorem:
Magnitude = √(North-south component^2 + East-west component^2)
= √((-3.446698km)^2 + (137.194km)^2)
≈ 137.47km
To find the direction, use the inverse tangent function (arctan):
Direction = arctan(East-west component / North-south component)
= arctan(137.194km / -3.446698km)
≈ -88.875 degrees (measured clockwise from the positive y-axis)
Therefore, the total vector sum is approximately 137.47km at an angle of -88.875 degrees from the positive y-axis.