Max Range of Projectile on Non-Level Ground

In summary, the conversation is about finding an equation to calculate the maximum range of a projectile that is not on level ground. The person asking for help has attempted to solve it by making a diagram and substituting values, but has not been successful. The suggestion is to substitute values for y and x in the parabolic equation for the projectile, and to find the turning point of the function to calculate the maximum range.
  • #1
tman1
9
0
My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
 
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  • #2
tman1 said:
My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
I think the best thing you can do is post whatever you have done. I could suggest a lot but I don't know what is making you go wrong.

The Bob (2004 ©)
 
  • #3
Substitute
[tex]y=R\ sin\alpha[/tex]
and
[tex]x=R\ cos\alpha[/tex]
in the parabolic equation for the projectile.
The range will then be a function of [itex]\theta[/itex].The turning point of a function occurs where the derivative is zero...
 
Last edited:

1. What factors influence the max range of a projectile on non-level ground?

The max range of a projectile on non-level ground is influenced by several factors, including the initial velocity of the projectile, the angle at which it is launched, the height of the launch point, and the presence of air resistance.

2. How does the angle of launch affect the max range of a projectile on non-level ground?

The angle of launch has a significant impact on the max range of a projectile on non-level ground. In general, the optimal angle for maximum range is 45 degrees, as it allows for the most balanced combination of horizontal and vertical components of the projectile's motion.

3. Can air resistance affect the max range of a projectile on non-level ground?

Yes, air resistance can significantly impact the max range of a projectile on non-level ground. The presence of air resistance reduces the horizontal distance traveled by the projectile, resulting in a shorter max range.

4. Why does the height of the launch point matter for the max range of a projectile on non-level ground?

The height of the launch point affects the max range of a projectile on non-level ground because it determines the initial vertical component of the projectile's motion. A higher launch point will result in a longer max range, as the projectile will have more time to travel horizontally before hitting the ground.

5. Is there a way to calculate the max range of a projectile on non-level ground?

Yes, there are several equations and formulas that can be used to calculate the max range of a projectile on non-level ground, taking into account factors such as initial velocity, angle of launch, and air resistance. These calculations can be complex, but they can provide an accurate estimate of the max range based on the given parameters.

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