Question

A cliff diver plunges from a height of 25 ft above the water surface. The distance the diver falls in t seconds is given by the function d(t) = 16t² ft. What is the distance the diver falls in 3 seconds?

Answer 1

To calculate the distance a cliff diver falls in 3 seconds, we substitute t=3 into the distance function d(t)=16t² to get d(3)=144 ft.

Step-by-step explanation:

The student's question involves calculating the distance fallen by a cliff diver after a certain amount of time using a given function. To find the distance the diver fell in 3 seconds, we simply substitute the value of t (time) with 3 seconds into the provided function.

The distance function is given by d(t) = 16t² ft. If we plug in t = 3 seconds, the calculation becomes:

d(3) = 16(3)²
= 16(9)
= 144 ft

So, the distance the diver falls in 3 seconds is 144 feet. This straightforward application involves substituting the time parameter into the function to determine the precise distance fallen, showcasing the use of mathematical models in quantifying physical phenomena like free-fall distances in real-world scenarios.