Projectile motion Projectile Motion Subject to Gravity Assumptions: No air resistance and so the horizontal motion is at constant velocity. An object is subject to gravitational acceleration g = 9.8 m/s2. Vertical motion is at constant acceleration.

Cartesian equation is a parabola.

Factors Affecting Projectile Motion What two factors would affect projectile motion? Angle of projection Magnitude of initial velocity Initial Velocity Angle

Examples of Projectile Motion Launching a Cannon ball

Features of Projectile Motion Maximum Height The highest point the object reaches. At this point, the object has no vertical velocity. Solving the j component of the velocity vector equal to 0 will find the time. Time of Flight Time taken from launch until the object lands. If the x-axis represents the ground, solving the j component of the position vector equal to 0 will find the time of flight. If the ground is represented by a curve, find the intersection of the path of the object with curve representing the ground. Range The distance from the where the object is launched to where it lands. If the x-axis represents the ground, the range is the i component of the position vector at the when the object lands. If the ground is represented by a curve, find the magnitude of the position vector at the time when the object lands. The maximum range occurs when the angle launched is 45°.

Maximum height of a projectile.   At the maximum height the vertical component of the velocity is zero. Time to maximum height and time of flight By symmetry the time of flight is twice the value of time to maximum height.

Range on the horizontal plane