The height of a ball thrown upward from the ground is given by the quadratic function

Question

h = 160t - 16
, where h is in feet and t is in seconds.

What is the reasonable domain for this function?
Responses
A {x: 0 ≤ x ≤ 10}{x: 0 ≤ x ≤ 10}
B {x: 0 ≤ x ≤ 160}{x: 0 ≤ x ≤ 160}
C {x: x ≥ 0}{x: x ≥ 0}
D all real numbers

Answer 1

To determine the reasonable domain for the function $h(t)=160t-16t^2$, we need to consider the physical context of the problem. The function describes the height of a ball thrown upward, which implies that:

1. Time $t$ cannot be negative since we start measuring time from the moment the ball is thrown (which is at $t=0$).
2. We also need to consider when the ball hits the ground (i.e., when $h=0$), which occurs at a certain positive time.

To find when the ball hits the ground, we set $h(t)=0$:

$$160t-16t^2=0$$ Factoring out $t$:

$$t(160-16t)=0$$ This gives us two solutions:

1. $t=0$ (the starting time)
2. $160-16t=0$ → $16t=160$ → $t=10$

Thus, the ball will be in the air from $t=0$ to $t=10$ seconds. Therefore, the reasonable domain of the function is the interval:

$$0\le t\le 10$$

This corresponds to option A: {x: 0 ≤ x ≤ 10}.