Find the resultant ir the sum of the displacement (1) 10m north west (2) 20m.30degree north of east (3) 35m due south
To find the resultant or sum of the displacements, we need to add the vectors together. First, let's represent each displacement as a vector.
(1) 10m north-west: We can break this displacement into two components - one in the north direction and one in the west direction. Since it is a north-west direction, the angle is 45 degrees with respect to the x-axis. Using trigonometry, we can find the components as follows:
North component = 10m * cos(45°) = 7.07m
West component = 10m * sin(45°) = 7.07m
So, the first displacement vector is (7.07m north, 7.07m west).
(2) 20m, 30 degrees north of east: This displacement is already given in terms of its magnitude and direction. We can use trigonometry to find its north and east components:
North component = 20m * sin(30°) = 10m
East component = 20m * cos(30°) = 17.32m
Thus, the second displacement vector is (10m north, 17.32m east).
(3) 35m due south: Since this displacement is purely in the south direction, we don't need to calculate any components. The third displacement vector is (35m south, 0m east).
Now, we can add the three vectors together to find the resultant. Let's add the north, east, and south components separately:
North component = 7.07m + 10m + 0m = 17.07m
East component = -7.07m + 17.32m + 0m = 10.25m
South component = 0m + 0m + (-35m) = -35m
Finally, we can combine the components to get the resultant vector:
Resultant vector = (17.07m north, 10.25m east - 35m south)
To express it in simpler terms, we can combine the opposite directions:
Resultant vector = (17.07m north, 10.25m east + 35m south)
Therefore, the resultant or sum of the displacements is approximately (17.07m north, 45.25m south-east).