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? round your answer to the nearest hundredth. about sec question 2 b. another gannet spots the fish at the same time, but it is only 84 feet above the water. it has an initial vertical velocity of -70 feet per second. which bird will reach the water first?

Answer 1

The gannet has about 2.75 seconds to swim away. The gannet that is 84 feet above the water will reach it first.

Step-by-step explanation:

To answer question a, we can use the equation for vertical motion: v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.

The initial velocity of the gannet is -88 ft/s, as it is flying downward. The acceleration due to gravity is -32 ft/s². We want to find the time taken, so we rearrange the equation to t = (v - u) / g.

Substituting in the values, t = (0 - (-88)) / -32 = 2.75 seconds. Therefore, the fish has about 2.75 seconds to swim away.

To answer question b, we can use the same equation and process as above, but with a different initial velocity. The initial velocity of the second gannet is -70 ft/s. Substituting the values, t = (0 - (-70)) / -32 = 2.19 seconds. Therefore, the gannet that is 84 feet above the water will reach it first.

Answer 2

To solve the problem, we use physics equations for uniformly accelerated motion. The time it takes for each gannet to reach the water is calculated by plugging their respective dive heights and initial velocities into the equation for uniformly accelerated motion, then comparing the two times to see which gannet reaches the water first.

Step-by-step explanation:

To determine how long the fish has to swim away and which gannet will reach the water first, we will use the physics equations for uniformly accelerated motion. For gannet A, which dives 100 feet with an initial velocity of -88 feet per second, we apply the equation s = ut + ½ at² to calculate the time it takes for gannet A to reach the water.

Substituting gannet A's values, we have:
100 = -88t + ½ (-32)t²

Solving this quadratic equation for t will give us the time for gannet A.

For gannet B, we repeat the process with 84 feet and an initial velocity of -70 feet per second. We'll compare the times for each gannet to determine which one reaches the water first. The bird with the smaller time value reaches the water first.