Basic Engineering Mathematics, Fifth Edition

274 Basic Engineering Mathematics

7. If velocity v 1 =25m/s at 60◦ and
   v 2 =15m/sat− 30 ◦,calculatethemagnitude
   and direction ofv 1 +v 2.


8. Calculate the magnitude and direction of the
   resultant vector of the force system shown in
   Figure 29.31.

308

158

608

6N

4N 8N

Figure 29.31

9. Calculate the magnitude and direction of
   the resultant vector of the system shown in
   Figure 29.32.

158

458

2m/s

4m/s

3.5m/s

308

Figure 29.32

10. An object is acted uponbytwoforces of mag-
    nitude10N and 8N at an angle of 60◦to each
    other. Determine the resultant force on the
    object.


11. A ship heads in a direction of E 20◦Sata
    speed of 20knots while the current is 4knots
    ina directionof N 30◦E. Determinethespeed
    and actual direction of the ship.

29.7 Vector subtraction

In Figure 29.33, a force vectorFis represented by

oa. The vector(−oa)can be obtained by drawing a

vector fromoin the opposite sense tooabut having

the same magnitude, shown asobin Figure 29.33; i.e.,

ob=(−oa).

b

2 F

F

a

o

Figure 29.33

For two vectors acting at a point, as shown in

Figure 29.34(a), the resultant of vector addition is

os=oa+ob

Figure 29.33(b) shows vectors ob+(−oa) that is,

ob−oaand the vector equation isob−oa=od.Com-

paringodin Figure 29.34(b) with the broken lineab

in Figure 29.34(a) shows that the second diagonal of

the parallelogram method of vector addition gives the

magnitude and direction of vector subtraction ofoa

fromob.

(a) (b)

2 a a

bsd b

o a o

Figure 29.34

Problem 11. Accelerations ofa 1 = 1 .5m/s^2 at

90 ◦anda 2 = 2 .6m/s^2 at 145◦act at a point. Find

a 1 +a 2 anda 1 −a 2 by (a) drawing a scale vector

diagram and (b) calculation

(a) The scale vector diagram is shown in Figure 29.35.

By measurement,

a 1 +a 2 = 3 .7m/s^2 at 126◦

a 1 −a 2 = 2 .1m/s^2 at 0◦

(b) Resolving horizontally and vertically gives

Horizontal component ofa 1 +a 2 ,

H= 1 .5cos90◦+ 2 .6cos145◦=− 2. 13