Projectile launched horizontally

For any projectile launched horizontally, the projectile is given an initial horizontal velocity. The cannonball will also accelerate horizontally due to free fall. The goal of this lesson is to show you the trajectory of the cannonball.

The initial vertical velocity is of course equal to 0. 

For, example, let's say that you launch a cannonball horizontally as shown in the picture above. 

Once the cannonball is in the air, there are two things happening with the cannonball at the same time.

The cannonball will be affected by the horizontal speed and the vertical speed. 

How to find the path of a projectile launched horizontally using the vertical speed and the horizontal speed

First, let us talk about the horizontal speed. Notice that there is no horizontal acceleration because there is no horizontal force acting on the cannonball . With no horizontal acceleration, the cannonball will move horizontally with constant velocity.

Below, we show constant velocity for the cannonball by using vectors that have the same size.

Constant horizontal speed of a cannonball

Second, as the cannonball move horizontally, gravity will force the cannonball to fall vertically as well. Therefore, the cannonball will experience free fall. We saw in the lesson about free fall that objects in free fall accelerate.

This means that the speed is not constant, but keep on increasing. Since the speed is increasing, the object will cover a greater distance in each successive equal time interval. Below, we show a speed that is increasing as the cannonball experiences free fall.

Vertical speed of a cannonball

We can combine the vertical and horizontal movement/speed of the cannonball to see what we end up with. See below the horizontal speed, the vertical speed, and the resultant speed in red. The ball move along the green curve which is a parabola. The vectors shown in red (resultant speeds) are tangent to the green curve although it does not look perfect.

Trajectory of a cannonball launched horizontally

Important things to keep in mind when a projectile is launched horizontally

The path traced above in green is the path that a projectile will follow when the following conditions are met.

  • The projectile is accelerating only in the vertical position only.
  • Air resistance is negligible or not important. Air resistance is not important when the object is very heavy or the object is moving slowly.

Next, we learn about the path and speed of a projectile launched at an angle.

Quiz about projectile launched horizontally

This projectile launched horizontally quiz will help you see how the velocity and acceleration behave when the projectile is launched horizontally. You will not need to use a paper and pencil to complete this quiz. 

First, read the lesson about projectile launched horizontally and then take this quiz.

Objective of the quiz:

  • recognize the path of projectiles launched horizontally.
  • See how the horizontal velocity and the horizontal acceleration behave.
  • See how the vertical velocity and the vertical acceleration behaves.
  • Understand when air resistance is negligible.

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