We know that the stone's velocity was −152 ft/s when it hit the ground. Therefore, since v(t) = −32t, the time when the stone hit the ground wast = s.

Break Down the Problem

1. We are given the velocity function of the stone as $v(t) = -32t$.
2. We need to find the time $t$ when the velocity $v(t)$ is equal to −152 ft/s.

Relevant Concepts

1. The relationship between the velocity and time is given by the equation $v(t) = -32t$.
2. To find $t$, we will set $v(t) = -152$ and solve for $t$.

Analysis and Detail

1. Set the velocity equal to -152: $-32t = -152$
2. To solve for $t$, divide both sides by -32: $t = \frac{-152}{-32}$
3. Simplifying this fraction: $t = \frac{152}{32}$
4. Reduce the fraction: $t = \frac{19}{4} \text{ or } 4.75 \text{ seconds}$

Verify and Summarize

1. The calculations show that $t = 4.75$.
2. We can double-check by substituting $t$ back into the velocity equation.
   • If $t = 4.75$: $v(4.75) = -32 \times 4.75 = -152 \text{ ft/s}$ This matches the condition when the stone hit the ground.

Final Answer

The time when the stone hit the ground was $t = 4.75$ seconds.