A stranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. The flare has an initial vertical velocity of 1500 feet per second. Its height is defined by the quadratic function below. Assume that the flare is fired from ground level. If the plane is flying at a height of 30,000 feet, a speed of 880 feet per second, and is 50,000 feet from the flare when it is fired, will the flare hit it? If so, tell when this will happen. If not, tell when the flare reaches the plane’s altitude.

Question

A stranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. The flare has an initial vertical velocity of 1500 feet per second. Its height is defined by the quadratic function below. Assume that the flare is fired from ground level. If the plane is flying at a height of 30,000 feet, a speed of 880 feet per second, and is 50,000 feet from the flare when it is fired, will the flare hit it?  If so, tell when this will happen. If not, tell when the flare reaches the plane’s altitude.