a man travels 7km 40° west of north, then 10km east. find the resultant displacement
convert from polar to rectangular form
add the x- and y-components to get the resultants
Then find the magnitude in the usual way.
what do you get?
Hi
To find the resultant displacement of the man's journey, we can break down the distances and directions into their horizontal (x) and vertical (y) components.
First, let's find the x-components:
- Traveling 7 km at 40° west of north means the man is moving in the northwest direction. The x-component can be determined by finding the horizontal projection of the 7 km distance: 7 km * cos(40°) = 5.358 km
Next, let's find the y-components:
- Again, traveling 7 km at 40° west of north means the man is moving in the northwest direction. The y-component can be determined by finding the vertical projection of the 7 km distance: 7 km * sin(40°) = 4.744 km
Now, let's find the displacement after traveling 10 km east:
- Traveling 10 km east means the man moved in the positive x-direction. Therefore, the x-component becomes: 5.358 km + 10 km = 15.358 km
- Since there is no change in the y-component, the y-component remains 4.744 km.
Finally, let's find the resultant displacement by combining the x and y components:
- The x-component is 15.358 km
- The y-component is 4.744 km
- Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement: sqrt((15.358 km)^2 + (4.744 km)^2) ≈ 16.083 km
Therefore, the resultant displacement of the man's journey is approximately 16.083 km.
All angles are measured CW from +y-axis.
D = 7[320o] + 10[90],
D = (7*sin320+10*sin90) + (7*cos320+10*cos90)l,
D = 5.50 + 5.36i = 7.7km[45.7o] CW.