A lorry had its windscreen shattered when someone threw a snowball or lump of ice at it in Ethiebeaton, north of Monifieth.
In another crime nearby, a 15-year-old boy was struck over the head with a bottle.
The incidents, which happened five days apart on the boundary of Dundee and Angus, are being investigated by Tayside Police.
The lorry was struck about 7pm on Wednesday as it was heading into Dundee on the A92.
As it was passing Ethiebeaton, where Dobbies Garden Centre and Angus Gateway are, the windscreen was struck by a snowball or lump of ice.
The windscreen was shattered but remained intact. The driver was unhurt.
There is no description of the person responsible.
Police are also investigating the assault on the teenager on the Seven Arches viaduct path at 9pm on Friday, December 17.
The 15-year-old was with friends walking along the path between Panmurefield Village and Grange Road in Monifieth when they were attacked by a youth thought to be slightly older.
The assailant struck the 15-year-old over the head with a bottle, causing a cut behind his left ear that required two stitches.
The attacker is described as aged 16, wearing a light blue jumper and dark jeans.
Anyone with information on either incident is asked to call Tayside Police on 0300 111 2222 or Crimestoppers on 0800 555 111.
Photo used under a Creative Commons licence courtesy of Flickr user House of Sims.