What is projectile motion?
Projectile motion is a type of 2d motion in which body moves in both x and y direction. When a body is thrown and moves under action of gravity in 2d motion so the motion is called projectile motion.
In absence of air resistance, the projectile involves constant acceleration downwards and constant horizontal velocity.
Projectile has a parabolic shape.
Assuming in projectile:
Three assumption are made to analyze the projectile motion:
1. The gravity is constant over the range of motion and always directed downward.
2. The air resistance is neglected.
3. The rotation of earth does not effect the motion.
Motion on x axis:
When a body is thrown at a certain angle it covers in both x and y axis. In x axis the initial velocity of the body remain constant it means there is zero acceleration. But there is air resistance opposing the motion of the body which is neglected. The initial velocity is represented by u so we can say that:
U = Ux = Ucos
Motion on y axis:
In y axis the gravity is acting downward which is replacing the acceleration it means there is some velocity acting downwards. The initial velocity in y axis will vary and represented by Uy.
When a body is thrown at certain angle with initial velocity u, so it simultaneously covers x and y direction.
X direction --> Ux = Ucosθ
Y direction --> Uy = Usinθ
Ux remain constant in whole trajectory and hence Ux equals to u.
But in y axis at every point velocity changes and hence there is acceleration due to gravity which is always negative and directed downwards.
At maximum height the y component of velocity becomes zero and velocity and acceleration are perpendicular to each other.
Total Time of flight:
Time of flight is time taken by body to complete the projectile motion. It can be calculated by following formula:
If the y component of velocity is not given, so we can use usinθ.
Maximum height of projectile
The maximum height of projectile occurs when vertical component of velocity becomes zero.
We can calculate maximum height of projectile by following formula.
Range of projectile:
Range is horizontal distance from starting point of trajectory to end point.
As range is horizontal component so will take total time of flight in derivation.
Maximum Range of projectile:
Maximum range of projectile can be obtained on optimum angle. When the angle is 45°, there will maximum range.
Hence projectile must be launched at angle 45° to attain maximum range. For all other angles greater or smaller than 45° the range will be less than Rmax.
Some terminologies:
Trajectory: Trajectory is a path followed by projectile in parabolic shape. Trajectory depends on launch angle and initial velocity.
Muzzle Velocity: It is velocity of body just after the launch of projectile.
Ballistic Projectile: It is a guided projectile in which the target is set used in missiles.
Vertical Projectile: It is projectile launched from certain height.
Vertical Displacement:
It is height of projectile at any point of trajectory. It can be found by second equation of newton.
Here the height will be negative as we are talking about depth.
Summary:
In absence of air resistance, the projectile involves constant acceleration downwards and constant horizontal velocity. 1. The gravity is constant over the range of motion and always directed downward. In x-axis the initial velocity of the body remain constant, it means there is zero acceleration. When a body is thrown at certain angle with initial velocity u, so it simultaneously covers x and y direction. The maximum height of the projectile occurs when the vertical component of velocity becomes zero. Hence, the projectile must be launched at angle 45° to attain maximum range.
