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In the experiment setup, the detector is connected to a polarized electric circuit, meaning there is a positive end and a negative end. Even though the velocity of the electron is 0, it would float up towards the positively charged part of the circuit near the detector (because opposite charges attract) and still hit the detector.
Although the threshold energy is zero, the detector for the experiment would still be able to detect when an electron is being emitted. The energy is constantly changing due to electrons being emitted, thus the metal will have a slight positive potential due to loss of electrons (even at 0 kinetic energy) which allows the detector to notice loss of electrons even when e(photon)=e(remove e-).
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