if he travels 7km N 30 degree E and 10km east find the resultant displacement
N: 7cos40
E: 7sin30+10
determine the values of those two.
Resultant^2=N^2 + E^2
Someone pls answer the question
To find the resultant displacement, we can use vector addition.
We have two displacement vectors: 7km N 30° E and 10km east. Let's break down the vectors into their horizontal (east-west) and vertical (north-south) components.
For 7km N 30° E:
- The vertical component is 7km * sin(30°) = 7/2 km ≈ 3.5 km north.
- The horizontal component is 7km * cos(30°) = 7√3/2 km ≈ 6.06 km east.
For 10km east:
- The vertical component is 0 km since it is purely horizontal.
- The horizontal component is 10 km east.
Now, we can add the horizontal and vertical components separately:
Horizontal component: 6.06 km + 10 km = 16.06 km east.
Vertical component: 3.5 km north + 0 km = 3.5 km north.
The resultant displacement is the vector formed by the sum of the horizontal and vertical components:
Resultant displacement = sqrt((horizontal component)^2 + (vertical component)^2)
= sqrt((16.06 km)^2 + (3.5 km)^2)
≈ sqrt(257.64 km^2 + 12.25 km^2)
≈ sqrt(269.89 km^2)
≈ 16.42 km
So, the resultant displacement is approximately 16.42 km at an angle of north of east.