The runner traveled 2km 22 degrees North East from y axis, 4km 25 degrees North West from x axis, 7km 70 degrees South West from y axis, 6km 50 degrees South East from y axis. what is the resultant displacement of the runner using resolution of vectors to its components
if you can resolve one vector, you can do four. Then just add them up...
2km 22 degrees North East from y axis
makes no sense. I assume you meant
2km @ N22°E = (2sin22°,2cos22°) = (0.75,1.85)
Resolve the others similarly, and then just add them up for a final (x,y) value.
Then the displacement is the usual √(x^2+y^2)
All angles are measured CW from +Y-axis,
Diisp. = 2km[22o] + 4km[295o] + 7km[250o] + 6km[130o],
X = 2*sin22+4*sin295+7*sin250+6*sin130 = -4.86 km,
Y = 2*Cos22+4*Cos295+7*Cos250+6*Cos130 = -2.71 km,
Disp. = Sqrt(X^2+Y^2),
Tan A = X/Y,
A = ?.
To find the resultant displacement of the runner using the resolution of vectors into its components, we need to break down each movement into its horizontal (x-axis) and vertical (y-axis) components.
First, let's analyze the given information:
1. The runner traveled 2km at 22 degrees North East from the y-axis.
2. The runner traveled 4km at 25 degrees North West from the x-axis.
3. The runner traveled 7km at 70 degrees South West from the y-axis.
4. The runner traveled 6km at 50 degrees South East from the y-axis.
Now, let's break down each movement into their respective x- and y-components.
For the first movement:
- Displacement: 2km at 22 degrees North East
- Horizontal component: 2km * cos(22 degrees) = 1.841 km
- Vertical component: 2km * sin(22 degrees) = 0.709 km
For the second movement:
- Displacement: 4km at 25 degrees North West
- Horizontal component: 4km * cos(25 degrees) = 3.539 km
- Vertical component: 4km * sin(25 degrees) = 1.712 km
For the third movement:
- Displacement: 7km at 70 degrees South West
- Horizontal component: 7km * cos(70 degrees) = -3.181 km (negative because it goes towards the negative x-direction)
- Vertical component: 7km * sin(70 degrees) = -6.799 km (negative because it goes towards the negative y-direction)
For the fourth movement:
- Displacement: 6km at 50 degrees South East
- Horizontal component: 6km * cos(50 degrees) = 3.863 km
- Vertical component: 6km * sin(50 degrees) = -4.594 km (negative because it goes towards the negative y-direction)
Now, let's calculate the overall x-component and y-component by adding up the respective components of each movement.
Summing up the x-components: 1.841 km + 3.539 km + (-3.181 km) + 3.863 km = 5.062 km
Summing up the y-components: 0.709 km + 1.712 km + (-6.799 km) + (-4.594 km) = -9.972 km
Therefore, the resultant displacement of the runner is approximately 5.062 km towards the positive x-axis and -9.972 km towards the negative y-axis.