Question

when an object is dropped, the distance it falls in t seconds, assuming that air resistance is negligible, is given by
s(t) = 16t²
where s(t) is in feet. suppose that a media’s reflex hammer is dropped from a hovering helicopter. find (a) how far the hammer falls in 4 sec, (b) how fast the hammer is traveling 4 sec after being dropped, and (c) the hammer’s acceleration after it has been falling for 4 sec.

(a) the hammer falls \boxed{} feet in 4 seconds.
(simplify your answer.)

Explanation:

Step1: Identify the distance function

The distance function is given as \( s(t) = 16t^2 \), where \( t \) is in seconds and \( s(t) \) is in feet. We need to find the distance fallen at \( t = 4 \) seconds.

Step2: Substitute \( t = 4 \) into the function

Substitute \( t = 4 \) into \( s(t) = 16t^2 \):

$$ s(4) = 16 \times (4)^2 $$

Step3: Calculate the value

First, calculate \( 4^2 = 16 \). Then multiply by 16:

$$ s(4) = 16 \times 16 = 256 $$

Answer:

256