Projectile motion on the moon

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 travelled 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?

Orodruin
Staff Emeritus
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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.

gneill
Mentor
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?

...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?