A man walks
5.0m
due east and then
10.0m
N30oE
. Find his resultant displacement
D = 5 + 10[30o]
X = 5 + 10*Cos30 = 13.66 m.
Y = 10*sin30 = 5 m.
D = sqrt(X^2+Y^2) = sqrt(13.66^2 + 5^2) = 14.5 m.
To find the resultant displacement of the man, we can break down his movements into two components: one in the east direction and one in the north direction.
First, let's find the east component:
The man walks 5.0m due east.
Next, let's find the north component:
The man walks 10.0m N30oE. To break this down into its north and east components, we can use trigonometry.
The north component can be found by taking the sin of the angle:
North component = 10.0m * sin(30o)
The east component can be found by taking the cos of the angle:
East component = 10.0m * cos(30o)
Now, let's calculate the values:
North component = 10.0m * sin(30o) = 10.0m * 0.5 = 5.0m
East component = 10.0m * cos(30o) = 10.0m * 0.866 = 8.66m (rounded to two decimal places)
To find the resultant displacement, we need to add the east and north components together:
Resultant displacement = Square root of ((east component)^2 + (north component)^2)
Resultant displacement = Square root of ((8.66m)^2 + (5.0m)^2)
Resultant displacement = Square root of (74.9956m^2 + 25.0m^2)
Resultant displacement ≈ Square root of 99.9956m^2
Resultant displacement ≈ 9.99m
Therefore, the man's resultant displacement is approximately 9.99m.
To find the resultant displacement of the man, we need to combine the two displacements given in the question.
The first displacement is 5.0m due east. This means that the man walks straight east for a distance of 5.0 meters.
The second displacement is 10.0m N30oE. This means that the man walks 10.0 meters in a direction that is 30 degrees east of north (N30oE).
To find the resultant displacement, we can break down the second displacement into its north and east components by using trigonometry.
The north component (N) can be found by multiplying the magnitude (10.0m) by the cosine of the angle (30 degrees):
N = 10.0m * cos(30°)
N ≈ 10.0m * 0.866
N ≈ 8.66m
The east component (E) can be found by multiplying the magnitude (10.0m) by the sine of the angle (30 degrees):
E = 10.0m * sin(30°)
E ≈ 10.0m * 0.5
E ≈ 5.0m
Now that we have the north and east components, we can find the resultant displacement by adding the east component to the initial east displacement:
Resultant displacement (R) = Initial east displacement + East component
R = 5.0m + 5.0m
R = 10.0m
So, the resultant displacement of the man is 10.0m due east.