Question

3. Determine the magnitude of the resultant vector uti using the Parallelogram method. Verify with the Head-to-Tail Method v=60N 38 u = 40N MCTAC: Mathematics for College Technology Module 4: Vectors and Geometry Lesson 18: Adding Vectors Using the Head-to-Tail and the Parallelogram Methods Vector ü has magnitude 30 M and vector i has magnitude 40N.. When placed tail-to-tail, the angle between i and V is 50° a) Determine the magnitude of the resultant vector ü + b) Determine the direction of the resultant vector ü +7

Answer 1

3) Using Parallelogram method., Both tails to meet- -60 Resultant (7) ütte o uoit collesse [esse mingei 38 & sin 38 u 400 40+ 60 Cos 38 Gocos 38") { + [to sin 38 38'j] นี้ 4 ปี 87.28 + 36.949 Verifying cusing Head-to Tail Method: с From the figure, x 7-60N 60c0938 BD Z 1380 co 60 sin38° t = 40N B Hence, IABI 2 (AB + BD) + (Co)? [40 +60 Cos 38°)” + [6o Sin 380) LABI 94.775

And .. C) O - tan AB + BD Gosin 38 tant [ 40 + Gocos 38 24.59° > Hence, (ABl caso i (ABl sind woj of ut. AB 94.775 cos 24.59 + 94.775 sin 24. 4.59° AB u tom 1.28 87- 36.947 Hence verified.

4) Pal z 30 1v1 - 40 . tail-to-tail augle 50°. ܢ 13 a) Hence, from figures shown. so both ale same, x q lal la tu tutu j lūlalu le plullulloso ·(30)** (40)”+ 2430140860550 2500 + 2400 COS 50° lutul 10 √ 25+ 24 cossoo 63.58 5) Direction of a tu reference vector u makes an the is If u angle soo wit a Hence, tant 40 sin so 30 + 40cos son , tari(0.55) Lł wrt u 0 | Angle of (u + 7) wort a 28.8

Answer 2

A= 100 N 40° N of W