Projectile Motion With Air Resistance Comparing the trajectory of an ideal projectile to that of one that experiences drag force.

2 Dimensional Motion Projectile motion is 2 dimensional motion in which objects moving horizontally while being accelerated vertically down by gravity Recall: Vector components V Vy Vx

Ideal Projectiles The initial velocity of a projectile launched at an angle should be resolved into horizontal (X) and vertical (Y) components. Horizontal component of motion is constant velocity. Vertical component of motion is uniformly accelerated. Y X

Ideal Trajectory: The parabolic trajectory can be modeled mathematically with simple algebra. The range or horizontal displacement can be calculated by hand. Air resistance is disregarded.

Real Projectiles Real projectiles experience air resistance Consequences: Actual X velocity is not constant nor is X acceleration Actual Y acceleration is not uniform. As a result the real range is smaller and the shape of the trajectory is different than in the ideal case in which range is predicted without air resistance.

Drag Force Drag force is always opposite the direction of motion. Fdrag = drag force magnitude (N) d = drag coefficient (kg/m3) CSA = cross sectional Area (m2) v = velocity (m/s) Drag force is always opposite the direction of motion.

Drag Force on Projectiles Drag force can be represented as one 2-dimensional vector or it can be expressed as its two 1-dimensional components. This is a baseball on the way up. Vy Fdx Vx g V Fdy Fd Y X

Drag Force on Projectiles This is the same baseball on the way down. Fd Fdy Fdx Vx g V Vy Y X

You will now use a spreadsheet to… Adjust the time increment to find the range of a projectile experiencing air resistance. Plot the ideal trajectory on the same axis as the real trajectory to compare their shapes. Accurately predict the range of a projectile fired from a 16’’ cannon on the USS New Jersey.

Troubleshooting/Tips The actual range (with air resistance) will be at the top of column O when it hits the ground (Y=0). To find the ideal range enter 0 for the drag factor (cell C2) and look in the same place. Highlight formulas as you write them into the spreadsheet. Look at the equation that each formula is referring to in order to better understand its meaning. Check each formula for accuracy after you have written it. Catching errors is going to save you some frustration if you need to search for a mistake.