The projectile motion is defined as the form of motion that is experienced by an object when it is projected into the air, which is subjected to the acceleration due to gravity. The projectile is the object while the path taken by the projectile is known as a trajectory.
When a particle is projected obliquely near the earth’s surface, it moves simultaneously in the direction of horizontal and vertical. The motion of such a particle is called Projectile Motion. In the above diagram, where a particle is projected at an angle θ, with an initial velocity u. For this particular case, we will calculate the following:
- The time is taken to reach point A from O
- The horizontal distance covered (OA)
- The maximum height reached during the motion.
- The velocity at any time “ t “ during the motion.
| Quantity | Value |
| Components of velocity at time t | vx = v0 cosθ0vy = v0 sinθ0–gt |
| Position at time t | x = (v0 cosθ0)ty = (v0 sinθ0)t – 1/2 gt2 |
| Equation of path of projectile motion | y = (tan θ0)x – gx2/2(v0cosθ0)2 |
| Time of maximum height | tm = v0 sinθ0 /g |
| Time of flight | 2tm = 2(v0 sinθ0/g) |
| Maximum height of projectile | hm = (v0 sinθ0)2/2g |
| Horizontal range of projectile | R = v02 sin 2θ0/g |
| Maximum horizontal range ( θ0 = 45° ) | Rm = v02/g |