Projectile Motion best angles

[Gustason]

Projectile Motion "best angles"

Homework Statement

Collect sufficient and relevant empirical data to support the claim that for any initial velocity V there is a "best angle" theta 0_ba that yields the largest horizontal displacement (change in x). Support the claim that there is a "best angle" that yields the largest hang time.
Describe why there is a best angle theta 0 _ba. Why do both smaller and larger launch angles give less horizontal displacement.

Homework Equations

Well I was just given this without any real explanation and thus I don't really know what equations to use. He mentioned that there are some websites that could help with this.

The Attempt at a Solution

I just need some help on how I can explain why there is a best angle and why smaller and larger launch angles give less horizontal displacement.

 

[Kurdt]

Have a play about on http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html" page. If you're familiar with the kinematic equations then you can set them up and try and solve for the greatest horizontal distance. or graph the distance as a function of angle.

 

[baba89]

As a scientist, it is important to approach this question with a systematic and evidence-based approach. In order to determine the "best angle" for projectile motion, we must first understand the factors that affect the horizontal displacement and hang time of a projectile.

The horizontal displacement of a projectile is affected by its initial velocity and launch angle. The hang time, or the time that the projectile remains in the air, is also affected by these same factors.

To gather empirical data, we can conduct experiments by launching projectiles at different angles and measuring the resulting horizontal displacement and hang time. By varying the initial velocity and keeping all other factors constant, we can determine the relationship between the launch angle and these two variables.

From these experiments, we can observe that the horizontal displacement is largest at a specific angle, known as the "best angle" or theta 0ba. This angle is typically around 45 degrees, but can vary depending on the initial velocity.

One explanation for why there is a best angle is due to the components of the projectile's motion. When a projectile is launched at an angle, its initial velocity can be broken down into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component changes due to the force of gravity.

At the best angle, the horizontal and vertical components are balanced, resulting in the maximum horizontal displacement. When the angle is smaller, the vertical component is larger, causing the projectile to spend more time in the air and resulting in a shorter horizontal displacement. On the other hand, when the angle is larger, the vertical component is smaller, causing the projectile to spend less time in the air and resulting in a shorter horizontal displacement.

Therefore, the best angle for maximum horizontal displacement is when the horizontal and vertical components are equal, resulting in the longest hang time and largest horizontal displacement.

In conclusion, through empirical data and scientific reasoning, we can support the claim that there is a best angle for maximum horizontal displacement and hang time in projectile motion. This angle is determined by the balance between the horizontal and vertical components of the projectile's motion, and is essential in understanding the behavior of projectiles.