Context. Dynamic features such as chromospheric jets, transition region network jets, coronal plumes, and coronal jets are abundant in the network regions of polar coronal holes on the Sun. Aims. We investigate the relationship between chromospheric jets and coronal activities, such as coronal plumes and jets. Methods. We analyzed observations of a polar coronal hole including the filtergrams taken by the New Vacuum Solar Telescope at the Hα − 0.6 Å to study the Hα jets, as well as the Atmospheric Imaging Assembly 171 Å images to follow the evolution of coronal activities. Results. The Hα jets are persistent in the network regions, with only some regions (denoted as R1–R5) rooted in discernible coronal plumes. With an automated method, we identified and tracked 1320 Hα jets in the network regions. We find that the average lifetime, height, and ascending speed of the Hα jets are 75.38 s, 2.67 Mm, 65.60 km s−1, respectively. The Hα jets rooted in R1–R5 are higher and faster than those in the others. We also find that propagating disturbances (PDs) in coronal plumes have a close connection with the Hα jets. The speeds of 28 out of 29 Hα jets associated with PDs are ≳50 km s−1. In the case of a coronal jet, we find that the speeds in both the coronal jet and the Hα jet are over 150 km s−1, suggesting that both cool and hot jets can be coupled. Conclusions. Based on our analyses, it is evident that more dynamic Hα jets could release their energy to the corona, which might be the result of a Kelvin-Helmholtz instability developing or that of small-scale magnetic activities. We suggest that chromospheric jets, transition region network jets, and ray-like features in the corona are coherent phenomena that serve as important vehicles for cycling energy and mass in the solar atmosphere.