Physics

The angle at which a projectile should be launched to achieve the maximum horizontal range is 45°.

 

Here's a detailed explanation of why a projectile should be launched at a 45° angle to achieve maximum horizontal range:

 

Projectile Components:

When a projectile is launched, its initial velocity can be divided into two components:

Horizontal Component ():

Vertical Component ():

Here, is the initial speed, and is the launch angle.

 

Time of Flight:

The total time the projectile is in the air is determined by its vertical motion. The vertical motion is influenced by gravity:

The time of flight can be expressed as:

This equation shows that time of flight depends on the vertical component of the initial velocity.

 

Horizontal Range:

The horizontal range can be calculated using the formula:

Substituting from the previous equation gives:

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