Page 167 - Standard Handbook Of Petroleum & Natural Gas Engineering

152 General Engineering and Science

(2-17)

The angle between the total velocity (or any other vector) and any particular
coordinate axis can be calculated from the scalar product of said vector and the unit
vector along that axis. The scalar product is defined as

a b = a,b, .t a,b, + a,b, = lallblcos0

where 8 is the angle between vectors a and b. Thus the angle between the velocity
and the x axis is
e, = cos-l[ $)

(2-18)

If the magnitude and direction of a vector are known, its components are the
products of the magnitude and the respective direction cosines. In the case of the
velocity vector, for example, the components are

vy = Ivplcosey (2-19)

I
vZ = v cosez
PI
Example 2-4

A projectile is fired at an angle of 30" to the surface of the earth with an initial
velocity of 1,000 ft/s (see Figure 2-9). What will be its velocity and the angle of its
trajectory as a function of time?

Figure 2-9. Diagram for Example 2-4.