# Gravitational Force

**PROJECTILES**

A projectile is any object which, once projected, continues its motion by its own inertia and is influenced only by the downward force of gravity.

Air resistance opposes motion both vertically and horizontally. It is tangential to the flight curve directly opposing the instantaneous velocity Vi

**Without air resistance:**

– Path is parabolic

**With air resistance**

– Doesn’t go as high

– Doesn’t go as far

– Not symmetrical

– Peaks earlier

When a projectile has a launch angle other than 0°, its launch velocity Vo must be broken up into its rectangular components to perform calculations. It is better to treat the launch velocity as two separate velocities.

**3 types of projectiles**

– Launch angle = 0°

so s = down

– Launch angle ≠ 0°

so s = 0m

– Launch angle ≠ 0°

so s = up or down

- A projectile with non-zero launch angle will be at a certain altitude at two separate times t1 and t2, once on the way up and once on the way down, unless that time is at the apex of its flight. Therefore, the solution for t is the quadratic formula for x:

- The final velocity of a projectile is the vector addition of its vertical and horizontal velocities. It has magnitude and direction.
- For projectiles with sv = 0 there are two angles which produce the same range, 45° – θ and 45° + θ
- Maximum range for projectiles with sv = 0 is achieved when launch angle = 45°
- When considering a situation with wind, add or subtract the wind velocity from the horizontal component of the launch velocity to determine the net forward velocity.