Page 168 - Standard Handbook Of Petroleum & Natural Gas Engineering

Dynamics 153

x Component: The initial velocity in the x direction is

vx = 866 ft/s

Assuming no air friction, this velocity is constant.
y Component: The initial velocity in the y direction is

v~<> 500 ft/s
=
In the y direction, the projectile has a constant acceleration of -g = -32.2 ft/sec:'.
Thus by Equation 2-2, Column, 2, Table 2-5, its velocity as a function of time is

vv(t) = v,~] + at = v,, -gt
32.2 ft
= 500 ft/S - -
S2

and the total velocity vector is

v = 8661+(500-32.2t)j
The angle of the trajectory is found from Equation 2-18 as

1
ex = cos-' 866
[866* +(500-32.2t)']05~

It is often convenient to use some other coordinate system besides the Cartesian
system. In the normal/tangential system (Figure 2-10), the point of reference is not
fixed in space but is located on the particle and moves as the particle moves. There is
no position vector and the velocity and acceleration vectors are written in terms of
n

PATH OF
MOTION

Figure 2-10. Normal and tangential unit vectors at different points on a path.