Question
Check Your Understanding
Question
Martha dives into a swimming pool from a diving board that is
feet above the water. Her initial upward velocity is
feet per second. The function
models Marthas height from the waters surface, where
represents time in seconds since she dove.
Complete the statements.
The interpretation of
is that at
, Marthas height is
from the waters surface.
Question
Martha dives into a swimming pool from a diving board that is
feet above the water. Her initial upward velocity is
feet per second. The function
models Marthas height from the waters surface, where
represents time in seconds since she dove.
Complete the statements.
The interpretation of
is that at
, Marthas height is
from the waters surface.
Answers
GPT-4o mini
To complete the statements, we need to identify what the function \( h(t) \) represents in terms of \( t \), which is the time in seconds since Martha dove. Typically, a function like this could be modeled in a standard form, such as:
\[ h(t) = -16t^2 + vt + s \]
where:
- \( -16t^2 \) represents the effect of gravity (in feet), assuming the acceleration due to gravity is 32 feet/second².
- \( v \) is Martha's initial upward velocity in feet per second.
- \( s \) is the initial height from which she dives (in feet).
Now, if we let’s assume that the function you are referring to as \( h(t) \) fits this model, we can fill in the blanks:
"The interpretation of \( h(0) \) is that at \( t = 0 \), Martha's height is \( s \) feet from the water's surface."
Let's say if \( s \) is the height of the diving board. For example, if Martha dives from a height of 10 feet above the water and her initial upward velocity is, say, 20 feet/second, then:
"The interpretation of \( h(0) \) is that at \( t = 0 \), Martha's height is 10 feet from the water's surface."
If you provide the specific values for the height and initial velocity, we can place those values in the completed statements.
\[ h(t) = -16t^2 + vt + s \]
where:
- \( -16t^2 \) represents the effect of gravity (in feet), assuming the acceleration due to gravity is 32 feet/second².
- \( v \) is Martha's initial upward velocity in feet per second.
- \( s \) is the initial height from which she dives (in feet).
Now, if we let’s assume that the function you are referring to as \( h(t) \) fits this model, we can fill in the blanks:
"The interpretation of \( h(0) \) is that at \( t = 0 \), Martha's height is \( s \) feet from the water's surface."
Let's say if \( s \) is the height of the diving board. For example, if Martha dives from a height of 10 feet above the water and her initial upward velocity is, say, 20 feet/second, then:
"The interpretation of \( h(0) \) is that at \( t = 0 \), Martha's height is 10 feet from the water's surface."
If you provide the specific values for the height and initial velocity, we can place those values in the completed statements.