# Projectile Motion

Show/Hide Sub-topics (Kinematics | A Level)

Projectile motion refers to the motion of an object that is projected into the air at an angle to the horizontal.

Assumption:

• Acceleration due to gravity, g, is constant (9.81 $\text{m s}^{-2}$) over entire motion and is always directed downwards.
• No horizontal acceleration
• Effect of air resistance is negligible

Path of projectile without air resistance (always a parabola)

Taking upwards as positive, (Click on image to enlarge)

Projectile motion with air resistance

Key Characteristics of Graph:

• Horizontal range of object is shorter
• Maximum height reached is smaller
• Path is asymmetrical about highest point

Horizontally,

• Horizontal velocity no longer constant
• Horizontal velocity decreases with time. Object slows down
• Smaller horizontal range

Vertically,

• Going up, $a_{\text{upwards}} \, = \, g + \frac{F_{\text{Drag} \, \text{Force}}}{m}$
• Going down, $a_{\text{downwards}} \, = \, g-\frac{F_{\text{Drag} \, \text{Force}}}{m}$

Since $\mid a_{\text{upwards}} \mid \, > \, \mid a_{\text{downwards}} \mid$, $\Delta V_{\text{upwards}} \, > \, \Delta V_{\text{downwards}}$. So, object slows down at a faster rate on the way up, time taken to reach maximum point is less than the time taken to reach the ground from the maximum point.

### 4 thoughts on “Projectile Motion”

1. I need to know what if the air resistance is not neglected Will The optimum angle be greater or less than 45 degrees

2. a canon ball is project so as to attain a maximum range. Find the maximum height attained if the initial velocity is U. pls can someone help with this question