Question

a ball is dropped from a height of 20 feet above the ground. The velocity v(s) of the ball after it has travelled a distance of s feet is modeled by the function v(s)=60s. what is the domain of the function v(s) in terms of the context?

Answer 1

We know that

The initial height is 20 feet above the ground.

The function to model the velocity is

$v(s)=60s$

Where s represents the distance in feet.

Mathematically, this function has all real numbers as a domain. However, that will no make sense for this situation, because it would use negative numbers for the distance s which does not make sense.

Therefore, the domain, in this case, would be all real numbers greater than or equal to zero, but less than or equal to 20.

The reason for this domain is that the ball will go from 20 feet above the ground to zero feet on the ground.

Using interval notation would be

$D\colon\lbrack0,20\rbrack$