Two vectors A and B have precisely equal magnitudes. For the magnitude of A+ B t

Question

Two vectors A and B have precisely equal magnitudes. For the magnitude of A+ B to be 100 times greater than the magnitude ofA B, what must be the angle between them Two vectors A and have precisely equal magnitudes. For the magnitude ofA to be greater than the magnitude of A-B by the factor w, what must be the angle between them A pirate has buried his treasure on an island with five trees located at the following points A(300 m 20.0 m), B(60,0 m, 800 m), Cf- 0.0 m, 0.0 m) D(4 80.0 m), and E( 700 m, 60.0 m). All points are measured relative to some origin, as in Fig ure Instructions on the map tell you to start at A and move toward B, but to cover only one-half the dis- tance between A and B Then, move toward C.covering one-third the disuance benween your current location and C. Next, move toward D, covering one-fourth the disuance between where you are and D. Finally, move to- ward E, covering one-fifth the distance between you and E, stop, and dig, (a) What are the coordinates of the point where the pirate's treasure isburied (b) Re Three vectors are oriented as shown in Figure PSSI where IAI 20.0 units, 40.0 units, and IBI ICI 30.00 units. Find (a) the xand ycomponents of the resultant vector (expressed in unit-vector nouation) and (b) the magnitude and direction of the resultant vector, IIA (600i 8.000 units, B 800i 5.000 units, and C (2001 19.0i) units, determine a and b such that aA An airplane flies 200 km due west from city A to city B and then 800 km in the direction 30.0 north of west from city B to city C (a) In straight line disuance, how lar is city Cirom city A? (b) Relative to city A. in what direction is city C A pedestrian moves 6.00 km east and then 13.0 km north. Using the graphical method, find the magnitude and direction of the resultant displacement vector Two vectors have unequal magnitudes. Can their sum be zero Explain. Tulsa has standard geographical coordinates of 36, 8 minutes North and 95 ,56 minutes West. Using a coordinate system centered at the center of the Earth, with az-axis going from the South Pole to the North pole, and an x-axis pointing through the 0° longitude line (meridian), determine the ocation for Tulsa,

Explanation / Answer

(1)

l A+B l = sqrt(A^2 + B^2 + 2*A*B*costheta)

l A - B l = sqrt(A^2 + B^2 - 2*A*B*costheta)

given A+B = n*(A-B)

sqrt(A^2 + B^2 + 2*A*B*costheta) = n* sqrt(A^2 + B^2 - 2*A*B*costheta)

squaring on both sides

(A^2 + B^2 + 2*A*B*costheta) = n^2* (A^2 + B^2 - 2*A*B*costheta)

also given lAl = lBl

( 1 + 1 + 2*costheta) = n^2*(1 + 1 - 2*costheta)

2 + 2*costheta = n^2*2 - n^2*2 - n^2*2*costheta

2*costheta*(n^2 + 1) = 2*(n^2-1)

theta = cos^-1(n^2-1)/(n^2+1)

for n = 100

theta = 11.42 degrees

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

3)

Ax = 0

Ay = +20

Bx = 40*cos45 = 28.3

By = 40*sin45 = 28.3

Cx = 30*cos45 = 21.21

Cy = -30*sin45 = -21.21

resultant

Rx = Ax + Bx + Cx

Rx = (0 + 28.3 + 21.21) = 49.51

Ry = (20 + 28.3 - 21.21) = 27.09 units

magnitude lRl = sqrt(Rx^2 + Ry^2) = 56.44 units

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

(4)

aA + bB + C =0

6ai - 8aj - 8bi + 3bj + 26i + 19j = 0

6ai-8bi - 8aj + 3bj = -26i - 19j

comparing i , j

6a - 8b = -26......(1)

3b - 8a = -19............(2)

solving 1 & 2

a = 5 <-------answer

b = 7 <-------answer

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

(5)

S1x = 200 km

S1y = 0

S2x = 300*cos45 = 212.13

S2y = 300*sin45 = 212.13

Sx = S1 + S1y = 200+212.13 = 412.13 km

Sy = S1y + S2y = 212.13 km

S = sqrt(Sx^2 + Sy^2)

S = 463.52 km

direction tan^-1(sx/sy) = 27.23 north of west

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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