Projectile Motion Without Trigonometric Functions

Abstract

In this paper we provide a treatment of projectile motion that is accessible to students who are unfamiliar with trigonometry but do have a minimal knowledge of elementary algebra and know the Pythagorean theorem. In this approach, we view the initial velocity of the projectile as being a combination of a vertical part (component) v0V and a horizontal component v0H (see Fig. 1). This is in contrast to the usual approach of taking the initial speed v0 and the launch angle as being given. We let the initial position be the origin and neglect air drag. Assuming that the constant acceleration kinematics equations are known, we may write vH = v0H, and the horizontal distance traveled is x = v0H t, where t is the elapsed time. We also have vV = v0V − gt, where g is the magnitude of the acceleration due to gravity. And the vertical displacement is y = v0V t − ½ gt2. These equations may be used to find the location and velocity of the projectile at any time t. We can also find the equation of the path of the projectile by combining Eq. [1(b)] and Eq. [2(b)] to get y = −(g2v0H2) x2 + (v0Vv0H) x, which is the equation of a concave-down parabola.