Kinematics. The problem about shooting a gun 2 or primitive ballistics
Again, we'll consider the problem of collection Svetozarova. At this time, a case of primitive ballistics.
Under the terms of this task, a gun and has a purpose. Imagine that gun and its purpose are the same distance l from each other. Question: after some amount of time a munition with an initial velocity v will hit the target? Air resistance can be neglected. The acceleration of free fall round up to ten meters per second squared.
We decided as follows:
To hit the target, you need to shoot at a certain angle (a). If you attach a coordinate axis, we see:
V = V * cos (a) * Vy = V * sin (a)
The x-axis acceleration in this case is not, and y-axis acceleration is equal to free fall, that is, 10 m / s2.
EXAMPLE V changes the equation on the y axis
Vy (t) = V * sin (a) - gt
An example of the equations of motion along the y axis
y (t) = V * sin (a) * t - gt2 / 2
And at the moment when the rise of the highest:
Vy (t) = 0V * sin (a) * - gt = 0t = V * sin (a) / g
The moment of falling to the ground
y (t) = 0V * sin (a) * t - gt2 / 2 = 0t = 2V * sin (a) / g
With a maximum height - let us substitute t when the highest rise:
h = V2 * sin2 (a) / 2g
Range - let us substitute t, just before the fall:
L = 2V2 * sin (a) * cos (a) / g = 2V2 * sin2 (a) / g