Question

Mikalee, a fighter pilot, ejects from her burning plane. Once she is safely on the ground, she launches a flare to attract the attention of a rescue plane. The initial velocity of the flare is 1600 ft/sec. The height of the flare, h(t), at any time, t, is modeled by the function h( t ) = − 16 t 2 + 1600 t . What is the maximum height of the flare?

Answer 1

To find a maximum, take the derivative of a function and set it equal to zero. The derivative in this case would be -32t+1600=0, therefore 1600=32t and t=1600/32. Plugging this back into the original equation we can get the height at this time, which is the maximun height.