Projectiles The only force acting on a projectile is the force due to gravity (weight).

Small enough to ignore b/c the effect is so small. Projectiles The only force acting on a projectile is the force due to gravity (weight). Fg For our course, we assume that air resistance is negligible. Small enough to ignore b/c the effect is so small.

Projectile trajectories Path

Projectile trajectories

Film the trajectory of a golf ball Parameters: Find the mass of the ball that you are using. The trajectory must be dropped or straight out (horizontally launched). The release height must be the height of the counters. You must ’see’ the ball in the frame from the launch to landing.

Projectile Quiz on Monday

Projectiles 51 Range Peak Height Launch Landing Definition: A projectile is an object moving through the air and the only force acting on it is the force due to gravity. Force Diagram for a Projectile: Fg The graphic above shows the VELOCITY VECTOR components at various places along the projectile’s trajectory. An object in free fall is a projectile. The horizontal and vertical components of a projectile’s motion are independent of one another. The acceleration of gravity causes the projectile to speed up, slow down or change directions vertically. Range Peak Height Launch Landing A projectile’s path is called its trajectory. The shape of the trajectory is parabolic. KEY CONCEPT: The acceleration of gravity does not affect the horizontal motion at all! Therefore, the horizontal motion of a projectile is at constant velocity. Special case about the range: When a projectile is launched at 45o, it reaches the maximum range. 51

LoggerPro Video analysis What was your projectile’s trajectory? Dropped? Launched Straight out? Import your film from last time into Complete the video analysis of the vertical motion. Do a curve fit (quadratic) to the data. Complete the video analysis of the horizontal motion. Do a linear fit to the data.

LoggerPro Video analysis Import your film from last time into Complete the video analysis of the vertical motion. Do a curve fit (quadratic) to the data. Complete the video analysis of the horizontal motion. Do a linear fit to the data. What was your projectile’s trajectory? Dropped? Launched Straight out? How are the ’y’ plots similar for dropped or launched straight out? How are the ‘x’ plots similar for dropped or launched straight out? How are the ‘x’ plots different for dropped or launched straight out? WHY?

LoggerPro Video analysis Import your film from last time into Complete the video analysis of the vertical motion. Do a curve fit (quadratic) to the data. Complete the video analysis of the horizontal motion. Do a linear fit to the data. What was your projectile’s trajectory? Dropped? Launched Straight out? How are the ’y’ plots similar for dropped or launched straight out? How are the ‘x’ plots similar for dropped or launched straight out? How are the ‘x’ plots different for dropped or launched straight out? WHY?

A B C

A B C Which of these graphs show a Launched Straight out projectile? Which of these graphs show a Dropped projectile? C

Great Stuff to know about Projectiles!! Predictable patterns in Projectile motion. 1. Vertical velocity at the peak is 0. 2. The magnitude of the vertical velocity is the same at symmetrical points on the trajectory, so |VyB| = |VyD| 3. The horizontal velocity is the same everywhere. 4. The time to go from A to C is equal to the time to go from C to E since A and E are ‘at the same level’. 5.The time to move from A to E is the same when analyzing horizontal or vertical motions. Peak Horizontal Motion Vx is constant. ΣFx = 0 Vertical Motion Vy changes. ΣFy ≠ 0 Since the horizontal forces are balanced, a projectile is in constant velocity in the horizontal direction. Since the vertical forces are unbalanced, a projectile accelerates in the vertical direction. We assume that friction is negligible.- that means it is so small that we can neglect it. Using “INTERVALS’ of motion: Many projectile problems are easier to solve if we analyze the up interval (Launch-to-peak) or down interval (peak –to-landing) instead of launch-to-landing. 56

Position(meters) Y (m) X (m) Time(seconds)

Position(meters) Y (m) A B C D X (m) Time(seconds)