Projectile Motion Physics Notes

Projectile Motion Physics Notes

Projectile Motion:
Projectile motion is a two-dimensional motion in which an object or particle is thrown upward at an angle to the horizontal and it moves along a curved path due to the action of gravity. The only force of significance that acts on the object is gravity, which acts downward.

The object projected into space or air is called a projectile and the path followed by the projectile is called a trajectory.

Following are a few examples of the projectiles:

• A bullet fired from a gun.
• A javelin or hammer was thrown by an athlete.
• A football kicked in air
• A piece of stone is thrown in any direction.
• A jet of water ejecting from a hole near the bottom of the water tank.
• An arrow was released from the bow.
• A missile deployed from a military aircraft from level flight.

Velocity and Acceleration in Projectile Motion
Projectile motion is a planar motion is which at least two position coordinates change simultaneously.

1. The motion of a projectile is a two-dimensional motion so, it can be discussed in two parts. Horizontal motion and vertical motion. These two motions take place independently of each other.
2. The velocity of the projectile can be resolved into two mutually perpendicular components; the horizontal component and the vertical component.
3. Acceleration changes velocity. If acceleration in a particular direction is zero then velocity in that direction remains the same. Thus, in projectile motion the horizontal component of velocity remains unchanged throughout the motion. The horizontal motion is a uniform motion.
4. The force of gravity continuously affects the vertical components so the vertical motion is a uniformly accelerated motion.

Projectiles can be thrown in various ways; on level ground, from a high tower to ground, from an airplane etc.

To study the motion of a projectile we assume that:

• There is no friction due to air
• The effect due to the curvature of the earth is negligible.
• The entire trajectory is near the surface of the earth.

Path of a projectile:
Let OX be a horizontal line on the ground and OY be a vertical line: O is the origin for X and Y-axis.

Consider that a projectile is fired with velocity u and making an angle θ with the horizontal from the point ‘O’ on the ground [figure]

The velocity of projection of the projectile can be resolved into the following two components

• u_x = u cos θ, along OX
• u_y = u sin θ, along OY

As the projectile moves, it covers distance along the horizontal due to the horizontal component u cos0 of the velocity of projection and along vertical due to the vertical component u sin0. Let that any time t, the projectile reaches the point P, so that its distances along the X and Y-axis are given by x and y respectively.

Motion along horizontal direction: If we neglect the friction due to air, then the horizontal component of the velocity i. e., u cos0 will remain constant. Thus

Initial velocity along the horizontal, u_x = u cos θ
Acceleration along the horizontal, a_x = 0
The position of the projectile along the X-axis at any time t is given by

Motion along vertical direction:
The velocity of the projectile along the vertical goes on decreasing due to the effect of gravity

Initial velocity along vertical, u_x = u sin θ
Acceleration along vertical, a_y = -g

The position of the projectile along the Y-axis at any time t is given by

This is an equation of a parabola. Hence the path of a projectile projected at some angle with the horizontal direction is a parabola.

Physics Notes