Question

--WILL MEDAL AND FAN--
a man drops a quarter from his apartment window several stories above the ground. The function h=-16t +256 gives the height of the quarter k in feet, t seconds after he releases it.

a. how long does it take the quarter to reach the ground?
b. what are the reasonable domain and range for the function h?
my answers are probably wrong i had a= 4,16 sec
and b. 4-16

Answer 1

@davejavous

Answer 2

A) The initial height is the constant, which is 256ft. The coin hits the ground when the height above the ground is 0. Simply rearrange to find t
\[ 0 = -16t + 256 \]\[ 16t = 256 \]\[t = 16 \, seconds\]

B) The height above the ground cannot be less than 0, but cannot be above 256 because we're dropping a coin not throwing it up. The domain will be the values of t that permits this, which is:\[ D: [0, 16] \]

The range is the set of values that can come out of the height function. Differentiating tells us that the slope of the line h=-16+256 is negative.

Think about the line y=-x between -10 and 10. The smallest value of x gives the largest value of y, because the line has a negative gradient.

By putting the lowest value of our domain into the height function we will get the largest value of the range.

Putting the endpoints of our domain (0 and 16) into the function we get 256 and 0. The range is therefore: \[R: [0, 256] \]

Answer 3

The domain is all of the times we can have for the entire drop, and the range is all of the heights we can have throughout the drop.