Suppose you first walk A = 10.5 m in a direction theta1 = 15 degree west of nort

Question

Suppose you first walk A = 10.5 m in a direction theta1 = 15 degree west of north and then B = 21.5 m in a direction theta2 = 36.00 south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B, as in the figure below, then this problem finds their sum R = A + B. Give the direction in degrees south of west.) distance m direction south of west

Explanation / Answer

Here ,

A = 10.5 * (sin(15) i + j * cos(15))

A = 10.14 j -i 2.72 m

B = 21.5 *( -cos(36) i - j * sin(36))

B = -17.3 i - 12.64 j

Now, for the resultant

R =A + B

R = 10.14 j -i 2.72 -17.3 i - 12.64 j

R = -20.02 i -2.5 j

magnitude of R = sqrt(20.02^2 + 2.5^2)

magnitude of R = 20.2 m

theta = arcatn(2.5/20.02)

theta = 7.1 degree

the distance is 20.2 m at 7.1 degree south of west

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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