Question

A gannet is a bird that feeds on fish by diving into the water. an gannet spots a fish on the surface of the water and flies down 100 feet to catch it. the bird plunges toward the water with an initial vertical velocity of -88 feet per second. a. how much time does the fish have to swim away?

Answer 1

The fish has approximately 3.125 seconds to swim away.

Step-by-step explanation:

To find the time the fish has to swim away, we need to determine the time it takes for the gannet to reach the water. We can use the equation:

h = vi * t + (1/2) * g * t^2

where h is the distance, vi is the initial vertical velocity, g is the acceleration due to gravity, and t is the time taken. Since the bird flies down 100 feet, h = -100 feet. vi = -88 feet per second and g = 32 feet per second squared. Plugging in these values, we get:

-100 = -88 * t + (1/2) * 32 * t^2

Simplifying the equation, we have:

0 = 16 * t^2 - 88 * t - 100

Solving this quadratic equation, we find two solutions for t:

t = 3.125 seconds and t = -1.375 seconds (not a valid solution)

Therefore, the fish has approximately 3.125 seconds to swim away.