Ahorse trots 17 miles north and then turns and trots 24 miles at an angle of 40° west of north. find the resultant displacement and direction mathematically. hint: this is a non-perpendicular vector problem.

 Resultant displacement = 38.58 miles at an angle of 23.57° north of west.

Explanation:

Let north represent positive y direction and east represent positive x direction. Unit vector along x direction is represented by i and vector along unit vector along y direction is represented by j

Initial displacement = 17 miles north = 17 j miles

Final displacement = 24 miles at an angle of 40° west of north = 24 miles at an angle of 130° to positive x -axis

                               = (24 cos 130 i + 24 sin 130 j )

                               = (-15.43 i + 18.36 j ) miles

Total displacement = 17 j + (-15.43 i + 18.36 j) = -15.43 i + 35.36 j

Magnitude of displacement

Angle to positive x -axis = tan⁻¹(35.36/-15.43) = 113.57°

Resultant displacement = 38.58 miles at an angle of 23.57° west of north.

in this image, you can see solar radiation going through ocean water.

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weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards