Gravity and Projectiles Projectile Any object that moves through the air or space under the influence of gravity continuing in motion by its own inertia Projectile Motion Without gravity a tossed object follows a straight line path With gravity the same object tossed at an angle follows a curved path Projectile motion is a combination of a horizontal component no acceleration so the object travels the same distance each second Since there is no acceleration in the horizontal direction the horizontal velocity of the object does not change a vertical component acceleration due to gravity is acting on the object directed downward The distance the object travels each second on the way down increases by d 1 2gt 2 And decreases by this much when the object is traveling upward Velocity increases each second by a factor of g when the object is traveling downward and decreases by a factor of g when the object is traveling upward The horizontal and vertical motions are independent of one another The horizontal motion and the vertical motion can be examined separately Projectiles launched horizontally Important points ball travels the same horizontal distance each second Curvature of path is the combination of horizontal and vertical components of motion Parabola where does this come from Curved path of a projectile that undergoes acceleration only in the vertical direction while moving horizontally at a constant speed Paths of a cannonball shot at an upward angle Vertical distance that a stone falls is the same vertical distance it would have fallen if it had been dropped from rest and been falling for the same about of time Paths of projectile following a parabolic trajectory Horizontal component along trajectory remains unchanged Only vertical component changes Velocity at any point is computed with the Pythagorean theorem Different horizontal distances Maximum range occurs for ideal launch at 45 degrees Without air resistance the time for a projectile to reach maximum height is the same as the time for it to return to its initial level Range and Maximum height of a Projectile The range R is the horizontal distance of the projectile when projectile is at the same position horizontally that it started at The maximum height the projectile reaches is h h v i 2 sin 2 i 2g only for symmetric motion R v i 2 sin 2 i g only for symmetric trajectory Projectiles shot at complementary angles will hit the same point but have different maximum heights