How do I calculate the force needed to hit a certain target from a certain angle?

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#1

I’m making a game around firing a cannon and getting more distance as the gun is upgraded.

My initial thought was to have a force number and somehow apply it to a Bezier curve to hit a point that is not explicitly predetermined, but I realized it might have been too complicated. (I would still like help on this!)

I changed my mind, and instead went for a system like hitting a specific zone (in picture) with the zone’s distance from the player tower distance being upgraded as the player progresses.

I want to know how much force I would need to apply to my projectile in order to have a flatter arc (also in picture) and hit the zone predetermined through upgrades, and somehow have the arc’s impact point be scaled with the tower’s height being upgraded.

Ideal curve/projectile trajectory example:

image
image1920×780 41.2 KB

(It would be somewhat similar to the game “Be a Paper Airplane”, in a sense that there is distant range and tower height involved)

Edit: Here is an oPhysics simulation for a more mathematical perspective:

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#2

Assuming the trajectory starts off perfectly horizontally, the time which the projectile is airborne can be calculated using the equation:
Vertically,
image
Initial velocity, u, = 0 since it’s perfectly horizontal since there’s no velocity acting vertically.
therefore the time airborne,
image
where s is the displacement between the turret and the ground and a is the gravitational acceleration.
Since we have the time airborne, the range can be calculated by:
image
This is trivial since horizontal velocity remains constant in projectile motion.

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#3

I’m sorry, but how would I get the force needed for the projectile to hit the specified distance out of these equations, or how would this be translated into a force number/Vector3 for the first option?

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#4

Do you mean an impulse? In projectile motion, there is no sustaining force other than the weight of the projectile.

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#5

Yes, sorry. I meant the impulse. Would this be the starting velocity from the oPhysics simulation linked in the original post?

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#6

the following equations can be rearranged to get
image

You can easily apply this to 3d since you can think of it as a 2d plane in a 3d world.

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#7

To clarify, Sh would be the initial velocity, which would be divided by the time airborne?

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#8

No, Sh is the horizontal displacement, Vh is the intial velocity.

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#9

So the initial velocity is the horizontal displacement divided by the time airborne, but the horizontal displacement is the initial velocity (which is being calculated) multiplied by the time airborne? (P.S. I am sorry if this should be a simple thing, I haven’t learned too much about physics yet.)

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#10

No, the horizontal displacement is not the initial velocity. It’s the vertical distance between the turret and the ground.