RE: 'cowl' on trainer broke
What type of plane is it?
It should not be hard to fix peel back the covering and glue or epoxy it back together. If you hit hard enough to damage the "cowl" check for damage to the firewall. Do not fly an airplane that has been in an accident until you check it over well for damage external and internal.
It is not a good idea to fly a plane with loose parts at any time, take the few minutes to make it right, and check your balance after any repairs or mods to the airframe.