4.5:
Projectile Motion
When an object is launched with some initial speed at an angle to the ground, it moves in a parabolic path due to gravity. The object is called the projectile, and the path it follows is called the trajectory.
The horizontal distance covered by the projectile is called the Range, whereas the maximum height, the projectile reaches, is known as the zenith of the trajectory.
The projectile's motion can be considered independent along the horizontal and vertical directions.
Assuming negligible air resistance, the only force acting on the projectile is due to the earth's gravity. So, the vertical component of acceleration, is equal to minus g.
The horizontal component of acceleration is zero. So, the projectile maintains a constant horizontal velocity.
The vertical component of the velocity, initially decreases, until the projectile reaches the zenith, at which point it becomes zero. It increases again as the projectile follows the downward trajectory.
However, the presence of air resists an object's motion, decreasing the horizontal velocity. The object's range and zenith are lesser than the path it would follow in a vacuum.
4.5:
Projectile Motion
An object thrown in the air follows a parabolic path under the influence of Earth's gravitational force. The motion of such an object is called projectile motion, and the object itself a projectile. The parabolic path followed by the projectile is called the trajectory. Some common examples of projectile motion are the launching of fireworks, a golf ball in the air, meteors entering the Earth's atmosphere, and the firing of bullets.
When an object falls under gravity and has no horizontal movement, it is called one-dimensional projectile motion. However, when there is horizontal and vertical motion, it is called two-dimensional projectile motion. Motions along the two perpendicular axes are independent and thus can be analyzed separately. Generally, the effect of air resistance is neglected when deriving two-dimensional projectile motion equations.
When analyzing two-dimensional projectile motion, the origin is considered to be the point where the projectile is launched. Since acceleration due to gravity always acts downward, the horizontal component of the projectile's acceleration is always zero throughout the trajectory. Similarly, the vertical component of velocity becomes zero when the projectile reaches the maximum height. Therefore, to solve equations of projectile motion, this choice of axes becomes highly convenient, and hence is widely used.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 1. pp 171-179. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-1/pages/1-introduction