Mechanics 2 - Projectiles

Projectiles have both Horizontal and Vertical motion;

Vertical Motion

• Vertical motion has Constant Acceleration of g=9.8ms⁻⁻²

Horizontal Motion

• The Speed of horizontal motion of projectiles is Constant
• The main formula for this type of motion is:

Distance = Speed * Time

• It is possible to find Velocity by differentiating Displacement with respect to Time:

v = dx / dt

• Acceleration can be found by differentiating Velocity with respect to Time:

a = dv / dt

   = d²x / dt²

• From this, Velocity can be found by integrating Acceleration with respect to Time:

v = ∫a dt

• And Displecement by integrating Velocity with respect to Time:

x = ∫v dt

This is another way to view the differentiations and integrations:

┏━━━━━━┓
┃Displacement┃
┗━━━━━━┛

 Differentiate ↓          ↑Integrate       

┏━━━━━━┓
┃    Velocity    ┃
┗━━━━━━┛

 Differentiate ↓          ↑Integrate       

┏━━━━━━┓
┃ Acceleration ┃
┗━━━━━━┛

In some cases, dots are used to show single or double differentiations (with respect to time);

If r = xi + yj then v = dr / dt = ṙ = ẋi + ẏj
       ‥    ‥    ‥
   and a = dv / dt = d²r / dt² = r = xi + yj

When integrating vectors with respect to time, the constant of integration is a vector:

v = ∫a dt

r = ∫v dt