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