Higher Engineering Mathematics, Sixth Edition

Vectors 259

resultant of the two forces, and the direc-

tion of the resultant with respect to the 12N

force.

[17.35N at 18. 00 ◦to the 12N force]

2. Velocities of 5m/s and 12m/s act at a point
   at 90◦to each other. Calculate the resultant
   velocity and its direction relativetothe12m/s
   velocity.
   [13m/s at 22. 62 ◦to the 12m/s velocity]


3. Calculate the magnitude and direction of the
   resultant of the two force vectors shown in
   Fig. 24.28.
   [16.40 N at 37. 57 ◦to the 13N force]

10 N

13 N

Figure 24.28

4. Calculate the magnitude and direction of the
   resultant of the two force vectors shown in
   Fig. 24.29.
   [28.43 N at 129. 30 ◦to the 18 N force]

22 N

18 N

Figure 24.29

5. A displacement vectors 1 is 30m at 0◦. A sec-
   ond displacement vectors 2 is 12m at 90◦.
   Calculate magnitude and direction of the
   resultant vectors 1 +s 2.
   [32.31m at 21. 80 ◦to the 30m
   displacement]


6. Threeforcesof5N,8Nand13Nact as shown
   in Fig. 24.30. Calculate the magnitude and
   direction of the resultant force.
   [14.72N at− 14. 72 ◦to the 5N force]

5N

13 N

8N

708

608

Figure 24.30

7. Ifvelocityv 1 =25m/sat 60◦andv 2 =15m/s
   at− 30 ◦, calculate the magnitude and direc-
   tion ofv 1 +v 2.
   [29.15m/s at 29. 04 ◦to the horizontal]


8. Calculate the magnitude and direction of the
   resultant vector of the force system shown in
   Fig. 24.31.
   [9.28N at 16. 70 ◦]

308

158

608

6N

4N 8N

Figure 24.31

9. Calculate the magnitude and direction of
   the resultant vector of the system shown in
   Fig. 24.32.
   [6.89m/s at 159. 56 ◦]