Projectile motion is the study of objects in free fall. A further definition by the department of basic education, is that projectile motion is the motion of an object in which the only force acting is the gravitational force. This topic helps to calculate the velocities and distance travelled by thrown objects. These objects are referred to as projectiles. To understand it, you need Grade 10 rectilinear motion and Grade 10 and 11 functions.
This section makes the following assumptions:
- Air resistance is ignored.
- Gravitational acceleration, \(g\) is constant and downward with the value \(9.8\text{ m}\cdot s^{-2}\)
- Earth's rotation is ignored
This section focuses on velocities at release/impact, distances/displacements travelled and the times it takes do these things. To pass exam questions you must:
- Apply equations of motion to find velocity, time and displacement.
- Interpret and draw \(v\) vs. \(t\), \(x\) vs. \(t\) and \(a\) vs. \(t\) graphs.
Key definitions:
Free fall: motion of an object under the influence of gravitational force only.
Projectile: an object moving under the influence of gravity only.
the equations of motion are:
\begin{alignat} {1} v_f &= v_i +a\Delta{t} \tag{1} \\ v_f^{2} &= v_i^{2} + {2}{a}\Delta{y} \tag{2} \\ \Delta{y} &= v_i\Delta{t} + \frac{1}{2}a\Delta{t}^2 \tag{3} \\ \Delta{y} &= (\frac{v_i+v_f}{2})\Delta{t} \tag{4} \\ \end{alignat}The following are points to consider for projectile motion calculation
- When an object is dropped, the initial velocity is zero
- When an object is thrown, it changes direction at maximum height.
- At maximum height, velocity is zero.
- When an object is thrown upwards, there is a time symmetry. This means the time it takes the object to reach maximum height is half the time it takes to return to the initial position.
We will cover calculations and more of projectile motion in future posts.