Mechanical Engineering Principles

LINEAR AND ANGULAR MOTION 133

S

0

N

W E

0 100 200 300

300 m/s

200 m/s

Scale : velocity in m/s

22 °

22 °

30 °

ab

b

ba

a

Figure 11.3

Problem 8. Two cars are travelling on

horizontal roads in straight lines, carAat

70 km/h atN 10 °Eand carBat 50 km/h at

W 60 °N. Determine, by drawing a vector

diagram to scale, the velocity of carA

relative to carB.

With reference to Figure 11.4(a),oarepresents the

velocity of carArelative to a fixed pointo,andob

represents the velocity of carBrelative to a fixed

pointo. The velocity of carArelative to carBis

given bybaand by measurement is 45 km/h in a

direction ofE 35 °N.

Problem 9. Verify the result obtained in

Problem 8 by calculation.

The triangle shown in Figure 11.4(b) is similar to

the vector diagram shown in Figure 11.4(a). Angle

BOAis 40°. Using the cosine rule:

BA^2 = 502 + 702 − 2 × 50 × 70 ×cos 40°

from which,BA= 45. 14

Using the sine rule:

50

sin BAO

=

45. 14

sin 40°

from which, sin BAO=

50 sin 40°

45. 14

= 0. 7120

S

N

W E

0 204060

Scale : velocity in km/h

a

70 km/h

50 km/h

45 km/h

(a)

o

60 °

b

A

50

70

45.14

(b)

O

q

60 °

40 °

60 °

B

35 °

10 °

Figure 11.4

Hence, angleBA 0 = 45. 40 °; thus, angle

ABO= 180 °−( 40 °+ 45. 40 °)= 94. 60 °,and

angleθ= 94. 60 °− 60 °= 34. 60 °.

Thusbais45.14 km/h in a directionE34.60°N

by calculation.

Problem 10. A crane is moving in a

straight line with a constant horizontal

velocity of 2 m/s. At the same time it is

lifting a load at a vertical velocity of 5 m/s.

Calculate the velocity of the load relative to

a fixed point on the earth’s surface.

5 m/s

2 m/s

5.385 m/s

o

b

a

q

Figure 11.5