Projectile Motion on the Moon: Finding the Optimal Launch Angle Using Equations

• Jonathan martin
In summary, the conversation discusses the maximum distance a cannon can shoot at different angles, assuming a constant initial velocity. The formula for calculating the maximum distance is given, but it is important to consider the assumptions and limitations of this formula, such as the constant gravitational field and the object's trajectory. The potential impact of exceeding the moon's escape velocity is also mentioned.
Jonathan martin

Homework Statement

A cannon can shoot whatever cannons shoot at different angles to the horizon, but with the same initial velocity. At what angle does the cannon shoot to a maximal distance? What would be that angle on the moon?

Homework Equations

• d is the total horizontal distance traveled by the projectile.
• v is the velocity at which the projectile is launched
• g is the gravity
• θ is the angle at which the projectile is launched
• y0 is the initial height of the projectile

The Attempt at a Solution

The maximum angle would be pi/4 (I am assuming), however if the projectile velocity was great enough to break the moon's escape velocity then the maximum distance could be given at an angle of pi/2. Thoughts?

Jonathan martin said:
The maximum angle would be pi/4 (I am assuming),
You cannot go around just assuming things. You need to do the math to back it up.

If you exceed the escape velocity the constant gravitational field will be a very bad approximation. Furthermore the object will not come down so it would be irrelevant to talk about the ”length” ofa shot.

The maximum range formula makes certain assumptions about its area of applicability (as do several other commonly employed physics formulas involving motion and energy) Do you know what the assumptions are?

Jonathan martin said:
...if the projectile velocity was great enough to break the moon's escape velocity then the maximum distance could be given at an angle of pi/2. Thoughts?
Yes that's certainly true. How does this notion tie in with the assumptions alluded to above?

What is projectile motion on the moon?

Projectile motion on the moon refers to the path that an object follows when it is thrown or launched into the air on the surface of the moon. It takes into account the gravitational force, air resistance, and the initial velocity of the object.

How does the gravity on the moon affect projectile motion?

The gravity on the moon is about 1/6th of the gravity on Earth. This means that objects will experience less gravitational pull and will travel further in the same amount of time compared to Earth. This also means that the trajectory of a projectile on the moon will be less curved and more linear.

What is the difference between projectile motion on the moon and on Earth?

The main difference is the strength of gravity. As mentioned before, the gravity on the moon is much weaker than on Earth, so objects will travel further and in a different trajectory. Additionally, there is no atmosphere on the moon, so there is no air resistance to slow down the object's motion.

How does the lack of atmosphere on the moon affect projectile motion?

The lack of atmosphere on the moon means that there is no air resistance to slow down the object's motion. This allows objects to travel further and faster compared to Earth, where air resistance can significantly affect the trajectory and speed of a projectile.

What factors affect projectile motion on the moon?

The main factors that affect projectile motion on the moon are the initial velocity of the object, the gravitational force, and the absence of air resistance. Other factors that can influence the motion include the shape and mass of the object, and the angle at which it is launched.

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