Alaina Gassler often saw her mother growing frustrated with blind spots when driving the family’s old Jeep Grand Cherokee in their Pennsylvania neighborhood.

The issue inspired Ms. Gassler, 14, to design a system that uses a webcam to show anything that might be blocked from a driver’s sight.

A panel of scientists, engineers and educators was so impressed with her prototype that she won the $25,000 top prize at the annual Broadcom MASTERS competition in Washington last week.

“I was shaking so much when they called my name because I did not expect it at all,” Ms. Gassler said Wednesday.