Electronic – diffrence between Energy measurement ADC and Bridge Sensor ADC

Trouble with ultrasound is that it doesn't stay in the box - you still have reflections from background. So for objects that are more than a few tens of cm from the sensor you need to do signal processing to find the target. In which case you might as well pick a solution using visible light to make it easier to debug. Computer vision tracking of moving objects against static background is a solved problem; see OpenCV for a free implementation. It works best against neutral backgrounds, but doesn't require that. Two cameras gives you stereo imaging and three positions.

If you just want ball speed along an axis you can get off-the-shelf radar guns for this purpose. Building your own radar system is an extremely difficult prospect.

Edit: 50m/s should have been in the original spec, that's quite fast. Ultrasonic usually works by sending out "chirps" and timing the response. Speed of sound is ~340m/s. So it takes 35ms for sound to traverse the 12m box. During that time a 50m/s target has moved 1.75m. You need to wait until your first pulse has gone out and back before sending the next, so pulse interval is at least 70ms. So you can only get one measurement every 3.5m.

You should also spec the latency: are you trying to interact with the moving object, or is it sufficient to work out where it was after is has passed? Do you care about the exact trajectory, or just speed of passing through the box (which can be found with doppler methods with ultrasound or radar).

1) If i wanted to make a circuit with a sensor that knows when any kind of metallic object is nearby, which kind of sensor would i have to use ?

You need to use a metal detector to detect a metallic object i.e. an object that can pass current or modify a magnetic field it comes into vicinity of. A metal detector generates an alternating magnetic field which will induce eddy currents into a metallic object. These eddy currents remove energy from the magnetic field and this is detectable. Non conducting materials like ferrite are also detectable because of the permeability of the material modifies the applied magnetic field in a different way to induced eddy currents. Metal detectors.

2) What kind of sensor do supermarkets use?

If you are talking about shop products that have a tag read this. These generally use a 13.56MHz magnetic field and operate very similarly to a metal detector.

3) how can i increase the detection distance of such sensors?

This can be done on metal detectors by spacing the transmit and receive coils out further and piling more electrical energy into the transmit coil. On RFID tags it's harder because the tag (the portable part) has to modify the imposed magnetic field in order to make itself detectable and with a larger incident field and coils further apart it rapidly becomes a really difficult job just to double the distance. Mag field reduces as a cube law so doubling the distance means 8 times less incident field and 8 times less received signal coming back. Net effect is a reduction in received signal relative to the incident signal of 64 : 1 (simplified math alert!). That's a big deal!!

4) how could i detect (for example) a car passing by the street with my sensor ?

Most car sensors are buried in the road and pretty much operate on the principles of metal detection.