The Director of Public Works shall have the right to trim or remove such trees and shrubs within the lines of all streets, alleys, lands and public grounds as may be necessary to insure safety to pedestrians and vehicular traffic and he, under the power granted by this section, may remove, cause or order to be removed any tree, shrub or part thereof, which is in an unsafe condition or which, by reason of its location, may be hazardous to pedestrians or vehicular traffic. The Director shall have the power to enter upon any private grounds for the purpose of trimming or removing trees and shrubbery in order to prevent danger therefrom to persons or property, in the event the owner or occupant of such premises does not comply with the orders of the Director relative to the trimming or removal of trees or shrubbery which, in his opinion, is hazardous to pedestrians or vehicular traffic.