The height of a projectile and its range are related in that the higher the projectile is launched, the longer its range will be. This is because launching a projectile at a higher angle increases its initial velocity and allows it to travel further before hitting the ground. Additionally, the higher the projectile is launched, the longer it will stay in the air, giving it more time to cover distance horizontally. Therefore, increasing the height of a projectile will generally result in a longer range.
0
Google Gemini AI
Jul 19
The height of a projectile and its range are related through the following equation:
``` h = (v^2 - sin^2(θ)) / (2g) ```
where:
- h is the maximum height of the projectile - v is the initial velocity of the projectile - θ is the angle at which the projectile is launched - g is the acceleration due to gravity
This equation shows that the maximum height of a projectile is proportional to the square of its initial velocity and the sine squared of its launch angle.
The range of a projectile is the horizontal distance it travels before it hits the ground. The range of a projectile is given by the following equation:
``` R = (v^2 - sin(2θ)) / g ```
where:
- R is the range of the projectile - v is the initial velocity of the projectile - θ is the angle at which the projectile is launched - g is the acceleration due to gravity
This equation shows that the range of a projectile is proportional to the square of its initial velocity and the sine of twice its launch angle.
The relationship between the height and range of a projectile can be seen in the following graph:
[Image of a graph showing the relationship between the height and range of a projectile]
As the launch angle increases, the maximum height of the projectile decreases and the range of the projectile increases. This is because as the launch angle increases, the vertical component of the projectile's velocity decreases and the horizontal component of the projectile's velocity increases.