A bridge is planned for a river as shown below. A surveyor sets up her equipment

Question

A bridge is planned for a river as shown below. A surveyor sets up her equipment at point O and establishes a coordinate system such that +x points due East and +y points due North. She determines the distance from point O to A is 1500 m, and the distance from point O to B is 2000 m. She also determines that line OB is 30 degree CCW from +x and line OA is 60 degree CCW from +x. 1. Use basic trigonometry to determine the coordinates for points A and B. Show appropriate units. 2. Express the position vectors r_OB, r_OA, and r_AB in Cartesian vector notation. Show appropriate units. 3. Using the figure provided below, we can say that r_OB = r_oA + r_AB. Rearrange the terms in this equation (as shown below) to confirm your answer for r_AB. Does r_AB = r_OB - r_OA?

Explanation / Answer

1)

from the figure

cos60 = xA/A

cos60 = xA/1500

xA = 750 m

sin60 = yA/A

yA = 1300 m

(xA , yA) = (750 , 1300 )

cos30 = xB/B ===> xB = 2000*cos30 = 1732 m

sin30 = yB/B ===>yB = 2000*sin30 = 1000 m

( xB , yB) = (1732 , 1000)

=================

roB = xB i + yB j = 1732i + 1000 j

roA = xAi + yA j = 750i + 1300 j

rAB = roB - roA

rAB = 1732i + 1000 j - ( 750i + 1300 j)

rAB = (1732-750)i + (1000-1300)j

rAB = 982 i - 300 j

-------------

3)

yes

rAB = roB- roA

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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