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?
- Initial velocity in the x-axis: v0x = 230 km/h = 63.8 m/s
- Horizontal distance from the launch: xf = 250 m
- Horizontal launch is studied as the composition of two motions. A uniform rectilinear motion in the x-axis, and a uniformly accelerated rectilinear motion in the y-axis (free fall)
- We will place the cannon on the y-axis at a height H which is the value we are looking for
- The value of the acceleration of gravity is 9.8 m/s2
- We will follow the normal sign convention for rectilinear motion
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.