Question

Share one physics equation that is relevant to a hand cannon(explain why)

Answer 1

The projectile motion equations are commonly used in artillery, because they allow to calculate at what angle should the cannon be aimed to hit a target. If the effects of the wind are neglected (although they are important, if we consider them the analytical solution becomes too complicated) then the only force acting on the cannon ball throughout the trajectory is the gravity. Let's consider that the origin of coordinates coincides with the point of launch, and the y direction points up, then:

The initial speed can be solved into components using the launch angle:

Then we can write:

And for the horizontal and vertical displacement of the cannon ball:

If we make y = 0 we can find the time that the cannon ball spends in the air before hitting the ground level (flight time):

And if we plug this expression in the horizontal displacement equation we get the range of the projectile:

Now the relevant equation: for shooting at a target wich is at a the same height and at a distance R away, knowing the speed at which the cannon can fire balls, the elevation angle of the hand cannon to hit the target must be:

Note that this equation has two solutions between 0° and 90°. The range is the same for this two angles but the maximum height and the flight time are greater for the larger angle.