anntenna

Hello, I recently bought a Uniden BC125AT to scan with in my truck. I also have a Uniden BC355N that I plan on installing in my truck. I primary scan ham and public safety channels (VHF-UHF 450-800 MHZ). The Tram 1089 I bought on Amazon works but does have the best range/clarity I am looking...

I am looking take a 102" whip and cut it down to 72.9" for use as a full wave receive only antenna at 162Mhz. The antenna will be placed on a tower at 320' AGL. If the antenna is RX only does it require a ground plane? I know the antenna will no longer be 50ohms will impedance miss match...