need help with physcis vector problem
Using combining vectors to find displacement problem(BEST answer)?
tourist on a jet ski move 1.2km 55 degrees North of E and then 3.15km 70 degrees south of east. determine the jet ski's displacement.
45
To find the displacement of the jet ski, we need to combine the two vectors given in the problem.
Step 1: Convert the given magnitudes and angles to their respective components.
For the first vector, moving 1.2 km 55 degrees North of East, we can break it down into its x and y components:
- The x-component is given by: 1.2 km * cos(55°)
- The y-component is given by: 1.2 km * sin(55°)
For the second vector, moving 3.15 km 70 degrees South of East, we can break it down into its x and y components:
- The x-component is given by: 3.15 km * cos(70°)
- The y-component is given by: -3.15 km * sin(70°) [negative sign indicates the south direction]
Step 2: Add the x and y components to get the resultant displacement vector.
The x-component of the resultant vector is the sum of the x-components of both vectors:
x-component = (1.2 km * cos(55°)) + (3.15 km * cos(70°))
The y-component of the resultant vector is the sum of the y-components of both vectors:
y-component = (1.2 km * sin(55°)) + (-3.15 km * sin(70°))
Step 3: Use the x and y components to find the magnitude and direction of the resultant vector.
The magnitude of the resultant vector can be found using the Pythagorean theorem:
magnitude = sqrt((x-component)^2 + (y-component)^2)
The direction of the resultant vector can be found using the inverse tangent function:
direction = atan(y-component / x-component)
By following these steps, you can find the displacement of the jet ski.