I wanted to make a radar system which will find the starting and ending degrees of an object, calculate the middle of the object and point a rubber band gun towards the middle and shoot at it.
Welcome to the forum
What is your programming and electronics experience ?
What size is the object?
What is the object made from?
Will there be other objects nearby?
How far away would the object be from the sensing system?
Strictly speaking Radar involves the use of radio frequencies.
For your project, you might find it easier to use an ultrasonic sensor, such as the ubiquitous HC-SR04.
There is a tutorial showing how to use that sensor at lastminuteengineers.com/arduino-sr04-ultrasonic-sensor-tutorial.
You could mount one on a servo motor, and slowly rotate it whilst taking distance measurements to find the position of the target.
It will be too expensive.
Consider using LIDAR. It's like RADAR except it uses a LASER instead of Radio frequencies.
Radar will give you a reflection of an object, but will have to be very sensitive to give you exact measurements of the object. It certainly won't give you depth. I can't see how you will determine where the center of an object is.
please tell us that both devices are NOT MOVING!
You also need to determine both the horizontal center and the vertical center to arrive at the middle of something. Also in reality, the floor/table, etc that the object is setting on will distort your center determination. So you will need to suspend the object.
With "objects" all around, how are you telling your system which is the right object. How it knows if the target object is floor, wall, box or cat?
Flicking elastic bands at an object is only a small step away from shooting a gun at the object. Can you assure up you are not going to do this?
Otherwise why flick an elastic band at anything?
I notice it is 22 hours since the first post and no other response from the OP.
Is this another one of those posters we have been talking about recently?
Yes.
Mathias Wandel did it.
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Hi,
The Rasp Pi does a lot of work, the Arduino just controls the servos under instruction from the Pi.
Google;
arduino sonar project
It may help if you experiment.
Tom.... 
Hi shadow_19832,
it was already mentioned LIDAR.
Measuring with laser distance sensors looking for me much more smart.
Some sensor to experiment with would be this (or similar) TOF sensor:
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