A group of physics students dropped a ball from the top of a 400-foot-high building and modeled its height as a function of time using the function H(t)=400−16t2 . The height, H , is measured in feet, and time, t , is measured in seconds. what is the domain

Answer 1

To determine the domain of the function \( H(t) = 400 - 16t^2 \), we need to consider the context of the problem:

1. Physical Context: The function models the height of a ball dropped from a building. The ball will fall until it reaches the ground, which means its height \( H(t) \) will reach 0.

2. Finding when the ball hits the ground: To find the time when the ball hits the ground, we set \( H(t) \) equal to 0 and solve for \( t \):

   \[ 0 = 400 - 16t^2 \] \[ 16t^2 = 400 \] \[ t^2 = 25 \] \[ t = 5 \text{ seconds} \]

   Since time cannot be negative in this context, we only consider \( t = 5 \).

3. Domain: The ball is dropped at \( t = 0 \) seconds, and it hits the ground at \( t = 5 \) seconds. Thus, the time \( t \) can take any value from 0 to 5 seconds, inclusive.

In conclusion, the domain of the function \( H(t) = 400 - 16t^2 \) is:

\[ \text{Domain: } [0, 5] \]

This means \( t \) can range from 0 to 5 seconds.