Delta r_1 + Delta r_2 + Delta r_3, from the origin. Categorize Despite the diffi

Question

Delta r_1 + Delta r_2 + Delta r_3, from the origin. Categorize Despite the difficulty in conceptualizing in three dimensions, we can categorize this problem as a substitution problem because of the careful bookkeeping methods that we have developed for vectors. The mathematical manipulation keeps track of this motion along the three Perpendicular axes in an organized, compact way, as we see below. To find the resultant displacement, add the three vectors: Delta r = Delta r_1 + Delta r_2 + Delta r_3 = (20 + 23 - 13)i cm + (35 - 14 + 15)j cm + (11 - 5 = (30)i + (36)j + (6)k cm Find the magnitude of the resultant vector: R = Squareroot R^2_x + R^2_y + R^2_z = 8.49 cm An ant crawling on a table undergoes three consecutive displacements: Delta r_1 = (4.5i + 2.8j)cm, Delta r_2 = (5.8i + 6.2j)cm, and Delta r_3 = (5.9i + 4.7j)cm. Find the magnitude and direction of the resultant displacement. magnitude cm direction degree counterclockwise from the + x-axis

Explanation / Answer

To find the resultant displacement add three vectors:

dr = dr1 + dr2 + dr3

dr = (4.5 + 5.8 + 5.9) i + (2.8 + 6.2 + 4.7) j

dr = 16.2 i + 13.7 j

magnitude of displacement"

|dr| = sqrt (16.2^2 + 13.7^2)

|dr| = 21.22 m

direction:

theta = arctan (Ry/Rx)

theta = arctan (13.7/16.2)

theta = 40.22 deg from +x-axis

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.