SOUTHWEST Airlines has sent passengers of Flight 1380 letters of apology — and cheques for $US5000 — in a bid to restore their confidence in the airline after an engine failure led to a passenger’s death.

About 20 minutes into its flight from New York City to Dallas, debris from the Boeing 737’s engine shattered a window, causing passenger Jennifer Riordan to be sucked partly through the fuselage.

Passengers dragged her back inside, but she died at a Philadelphia hospital after the crippled plane made an emergency landing with hero Captain Tammie Jo Shults, a former Navy flyer, at the controls.

“We value you as our customer and hope you will allow us another opportunity to restore your confidence in Southwest as the airline you can count on for your travel needs,” a letter to passenger Kamau Siwatu reads, according to CNN.

“In this spirit, we are sending you a check (cheque) in the amount of $US5000 ($6500) to cover any of your immediate financial needs,” read the letter.

In addition to the money, passengers will get a $US1000 ($1300) travel voucher “as a tangible gesture of our heartfelt sincerity,” according to the letter, which was signed by Southwest president Gary Kelly.

Such payments are not uncommon in such situations, said Mary Schiavo, a transportation lawyer and CNN analyst.

“It gets money in the hands of people that need it for counselling or something,” she said.

Federal authorities are investigating why a fan blade snapped off the plane’s left engine at 32,000 feet and penetrated the window.

America’s National Transportation Safety Board will look into how an interior crack on the blade led to the incident.

The crack, which was not detectable from the outside, was consistent with metal fatigue, NTSB chairman Robert Sumwalt has said.

“I know people would want answers right away. We would do a very methodical investigation,” Sumwalt said. “Right now, we just want to document everything that we can.”