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## Physics Tutorials

### Projectile Trajectory of a Cannonball

A projectile is a moving object that has only one force acting upon it: the force of gravity. The path it follows is called its trajectory. Projectiles travel with a parabolic trajectory because the force of gravity accelerates them downward from their otherwise straight-line, gravity-free trajectory. Neglecting air resistance, a projectile would maintain a constant horizontal velocity since there are no other horizontal forces acting on it. At the same time the downward force and acceleration results in a downward displacement from the position that the object would be if there were no gravity.

In other words, projectile motion has two components: horizontal and vertical, causing the trajectory of the projectile to curve. In the horizontal component, velocity is constant so it continues straight forward covering equal distances in equal times. At the same time, it is accelerating downward because of gravity, traveling larger downward distances in each successive time interval. These two simultaneous components create a curved path.

#### Application

Suppose a cannonball were shot from a cave. Its initial reaction would be to go in a straight line had there been no gravity. But since there is gravity, it causes a vertical acceleration which causes the ball to drop vertically below its otherwise straight line path which it would keep as mentioned in the law of inertia. Gravity acts as the downward force upon the projectile which influences its vertical motion. The cannonball falls more and more steeply, tracing out a parabolic trajectory.

#### Question

A car is driving at 2m/s down a straight highway. Sam shoots a bullet out of a gun vertically out of the sunroof relative to the car. If the car were to maintain constant velocity where would the bullet land (neglect air resistance)?

Answer: In the car. The force of gravity brings the bullet down; yet the constant horizontal component is keeps the bullet aligned with the car.

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