A typical light bulb can withstand a force of 15 N before it shatters. While changing a 0.025 kg light bulb, Mr. Kulik accidentally drops the bulb (from rest) onto a carpeted floor 2.3 m below. If the impact time with the carpet only lasts for 0.15 s, will the bulb most likely shatter or remain intact? Justify your answer with a calculation.