A horse trots 17 miles north and then turns and trots 24 miles at an angle of 40° west of north. Find the resultant displacement
1 answer:
Answer:
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.
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