5 Projectile Motion
Equations Introduced and Used in this Topic: (All equations are generally written and solved as vector and all variables are the same measures and units as Chapter 3)
All measures are separated into vertical and horizontal components and assume zero air resistance.
- Vertical Data
- [latex]\vec{a} = -9.80 \text{ m/s}^2[/latex]
- [latex]\vec{v_i} =[/latex]
- [latex]\vec{d} =[/latex]
- [latex]\vec{t} =[/latex]
- Horizontal Data
- [latex]\vec{v} =[/latex]
- [latex]\vec{d} =[/latex]
- [latex]t =[/latex]
Where…
- [latex]v[/latex] is average speed, commonly measured in metres/second (m/s) or kilometres/hour (km/h)
- [latex]\vec{v}[/latex] is average velocity, commonly measured in metres/second (m/s) or kilometres/hour (km/h) and includes a direction
- [latex]v_i[/latex] is initial speed, commonly measured in metres/second (m/s) or kilometres/hour (km/h)
- [latex]\vec{v_i}[/latex]is initial velocity, commonly measured in metres/second (m/s) or kilometres/hour (km/h) and includes a direction
- [latex]v_f[/latex] is final speed, commonly measured in metres/second (m/s) or kilometres/hour (km/h)
- [latex]\vec{v_f}[/latex] is final velocity, commonly measured in metres/second (m/s) or kilometres/hour (km/h) and includes a direction
- [latex]d[/latex] is distance traveled, commonly measured in metres (m), kilometres (km)
- [latex]\vec{d}[/latex] is change in displacement, commonly measured in metres (m), kilometres (km) and includes a direction
- [latex]a[/latex] is acceleration (deceleration is negative), measured in metres per second squared (m/s2)
- [latex]\vec{a}[/latex] is vector acceleration, measured in metres per second squared (m/s2) and includes a direction
- [latex]t[/latex] is Time, commonly measured in seconds (s) or hours (h)
| Equations | a | vt | vi | d | t |
|---|---|---|---|---|---|
| [latex]v_t = v_i+ at[/latex] | Not mentioned | ||||
| [latex]2_{ad} = v_{r}^{2} - v_{i}^{2}[/latex] | Not mentioned | ||||
| [latex]d = v_{i}t + \dfrac{1}{2} at^2[/latex] | Not mentioned | ||||
| [latex]d = \dfrac{(v_i + v_t)t}{2}[/latex] | Not mentioned |
5.1 Horizontally Launched Projectiles
- Extra Help: Characteristics of a Projectile’s Trajectory
- Extra Help: Horizontally Launched Projectile Problems
All measures are separated into vertical and horizontal components.
- Vertical Data
- [latex]\vec{a} = -9.80 \text{ m/s}^2[/latex]
- [latex]\vec{v_i} =[/latex]
- [latex]\vec{d} =[/latex]
- [latex]\vec{t} =[/latex]
- Horizontal Data
- [latex]\vec{v} =[/latex]
- [latex]\vec{d} =[/latex]
- [latex]t =[/latex]
The reason for breaking all data into vertical and horizontal components is that gravity acts vertically and as such, only affects the vertical motion. The horizontal motion remains constant until the point that air resistance begins to affect both the vertical and horizontal motion. At this point, the physics that we use in algebra breaks down for the analysis of projectiles.
Historically, the study of projectiles was one of the first t