Question
An object is dropped from a height h. it takes 6 seconds to hit the ground. if the velocity of sound is 1100 ft/s and the distance the object falls as a function of time is s=6t^2, what is the height h?
Answers
GPT-4o mini
To find the height \( h \) from which the object is dropped, we will use the equation for the distance fallen as a function of time, \( s = 6t^2 \), where \( s \) is the distance fallen and \( t \) is the time in seconds.
1. **Calculate the distance fallen in 6 seconds:**
\[
s = 6t^2
\]
For \( t = 6 \) seconds:
\[
s = 6(6^2) = 6 \times 36 = 216 \text{ ft}
\]
2. **Determine the height \( h \):**
Since the object is dropped from height \( h \) and falls a distance \( s \) during the fall, the height \( h \) is simply the distance fallen. Therefore, the height \( h = 216 \) ft.
Thus, the height \( h \) from which the object is dropped is:
\[
\boxed{216 \text{ ft}}
\]
1. **Calculate the distance fallen in 6 seconds:**
\[
s = 6t^2
\]
For \( t = 6 \) seconds:
\[
s = 6(6^2) = 6 \times 36 = 216 \text{ ft}
\]
2. **Determine the height \( h \):**
Since the object is dropped from height \( h \) and falls a distance \( s \) during the fall, the height \( h \) is simply the distance fallen. Therefore, the height \( h = 216 \) ft.
Thus, the height \( h \) from which the object is dropped is:
\[
\boxed{216 \text{ ft}}
\]