## Statement

difficulty

At what height, should you place a cannon capable of launching projectiles at an initial velocity of 230 km/h on the horizontal axis if you would like the projectiles to fall at a distance of 250 meters from where they are shot?

## Solution

Data

• Initial velocity in the x-axis: v0x = 230 km/h = 63.8 m/s
• Horizontal distance from the launch: xf = 250 m

Preliminary considerations

Resolution

The projectile moves with a uniform rectilinear motion in the x-axis. From the expression for the u.r.m. we can determine the time taken by the projectile to reach the x-coordinate of the specified point:

From the expressions for the y-axis (free fall) we can calculate the initial height at which the barrel must be placed so that exactly 3.91 seconds later it reaches the ground.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$x={x}_{0}+v\cdot t$
$y=\mathrm{H}-\frac{1}{2}g{t}^{2}$