The Range Equation is very useful expression for determine the maximum horizontal displacement, when a projectile lands on the same plane from which it was launched.
R = (vo^2 / g) sin (2 theta)
This relationship (derived below) has an interesting prediction (since there is a sine of 2 times the angle). Since the sine relationship is symmetrical from 0 to 180 degrees (about the 90 degree point), the sine of any angle less than 90 degrees is the same as the sine of its supplementary angle. That is, the sine of 80 = the sine of 100.
Since there is a double angle, you get equal sine values for (twice) a launch angle and (twice) the compliment of that angle. For example, the sine of 40 = the sine of 50.
You could also think of this as: you get equal ranges for angle 45 + or - the same amount. The range is the same for 30 and 60, 10 and 80, 35 and 55, etc.
Pretty neat, eh?
No comments:
Post a Comment