You gave the distance from the hospital to the launch site as 3.2 miles.Note the fragment of the rocket body blown into the air at 0:11. It hits the dirt at 0:26. One difference is that the Qassam rocket would have been launched at an angle, while the rocket in this video was supposed to go straight up. How far would the fragment have traveled if this rocket had been on an angled launch stand?
For a rocket to travel 3.2 miles in 15 seconds, it needs to travel at ~768 mph, which is almost exactly the speed of sound in dry air.
200 m/s is ~450 mph. These rockets are subsonic. The numbers don't work out.The Qassam's speed in the air is 200 meters per second