GEN PHYS 1 | Formulas and Solving Tricks

Notes

• Some formulas may look weird because of the subscripts.

Projectile Motion

Solving Tips

1. Write down the needed components for each the x and y components.

   • Acceleration is always -9.8 m/s² (due to gravity)

   • For projectiles launched horizontally, the initial vertical velocity always 0 m/s.

   • For projectiles launched at an angle,

     • the vertical velocity at the maximum height is 0 m/s and is also considered as the final velocity.

     • the overall airtime can be solved by multiplying the solved time by 2

2. Time is always the same for both components.

3. The x-component needs two available components to be solved.

4. The y-component needs three available components to be solved.

5. Check which y-component is neither given nor the RTF to decide which formula should be used.

Equations

Horizontal Motion

• \Delta x=v_{ix}t

Vertical Motion

• v_{y}=v_{iy}+at | missing ∆y

• \Delta y=v_{iy}t+\frac12at^2 | missing v_y

• v_{y}^2=v_{iy}^2+2a\Delta y | missing t

Overall Magnitude of Velocity

• v^2=v_{x}^2+v_{y}^2

• \theta=\tan^{-1}\left(\frac{v_{y}}{v_{x}}\right)

Launched at an Angle

Note: If overall magnitude of velocity is given

• v_{y}=v\sin\theta

• v_{x}=v\cos\theta

• t=\frac{v_{i}}{9.8}

  • 2t=2\left(\frac{v_{i}}{9.8}\right) (total air time)

• \Delta x=\frac{v_{i}^2\left(\sin2\theta\right)}{9.8}