Question

A ball is thrown directly upward from the ground with an initial velocity of 4.8 ft./sec. Represent the height of the ball from the ground t seconds after it was thrown upward using the model h(t).(1 point) Responses h(t)=−12⋅9.8t2+4.8t h left parenthesis t right parenthesis equals negative Start Fraction 1 over 2 End Fraction times 9.8 t squared plus 4.8 t h(t)=−16t2+4.8t h left parenthesis t right parenthesis equals negative 16 t squared plus 4.8 t h(t)=−12⋅4.8t2+4.8t h left parenthesis t right parenthesis equals negative Start Fraction 1 over 2 End Fraction times 4.8 t squared plus 4.8 t h(t)=−12⋅32t2+4.8t+4.8

Answer 1

Look at the answer choices again, thats not an opton?

Answer 2

yes it is an option

Answer 3

To find the height \( h(t) \) of a ball thrown upward, we can use the following kinematic equation that describes the height of an object under the influence of gravity:

\[
h(t) = -\frac{1}{2} g t^2 + v_0 t + h_0
\]

where:
- \( g \) is the acceleration due to gravity (approximately \( 32 \, \text{ft/s}^2 \) in the imperial system),
- \( v_0 \) is the initial velocity,
- \( h_0 \) is the initial height (which is \( 0 \) since the ball is thrown from the ground).

Given:
- The initial velocity \( v_0 = 4.8 \, \text{ft/s} \),
- The initial height \( h_0 = 0 \),
- The acceleration due to gravity \( g = 32 \, \text{ft/s}^2 \).

Applying these values into the equation, we have:

\[
h(t) = -\frac{1}{2} (32) t^2 + 4.8 t + 0
\]

This simplifies to:

\[
h(t) = -16 t^2 + 4.8 t
\]

Thus, the correct representation of the height of the ball after \( t \) seconds is:

\[
h(t) = -16 t^2 + 4.8 t
\]

So the appropriate response from your options is:

**h(t)=−16t^2+4.8t**

Answer 4

I apologize for any confusion. Let’s re-examine the answer choices provided:

1. \( h(t) = -12 \cdot 9.8t^2 + 4.8t \)
2. \( h(t) = -\frac{1}{2} \times 9.8 t^2 + 4.8 t \)
3. \( h(t) = -16t^2 + 4.8t \)
4. \( h(t) = -12 \cdot 4.8t^2 + 4.8t \)
5. \( h(t) = -\frac{1}{2} \cdot 32t^2 + 4.8t + 4.8 \)

From my calculations, the correct choice should relate to the formula for the height of the ball when thrown upward. Given that the acceleration due to gravity is approximately \( 32 \, \text{ft/s}^2 \), the correct format of the height function is based on that value.

The coefficient for \( t^2 \) in the equation should be \( -16 \), derived from \( -\frac{1}{2} \times 32 \), which leads us back to the earlier form of the equation \( -16t^2 + 4.8t \).

However, if we need to match one of the provided options closely, the second choice:

**\( h(t) = -\frac{1}{2} \times 9.8t^2 + 4.8t \)**

must be double-checked. The \( 9.8 \, \text{m/s}^2 \) corresponds to gravitational acceleration in metric units. In imperial units, using \( 32 \, \text{ft/s}^2 \) gives the \( -16 \) term.

If indeed this is a typo or mix-up in units, then based on what's typically done in imperial systems, the closest answer given the context would be option 3 as it incorporates the right approach for \( 32 \, \text{ft/s}^2 \):

Thus, the option would theoretically be:

**h(t) = −16t^2 + 4.8t**

If it's not an option, I apologize for the oversight. Please verify the question's context and selection, or clarify if there's any other set of values to assess.

Answer 5

Thank you for your patience. Given that the correct equation derived was \( h(t) = -16t^2 + 4.8t \), and you confirmed that this is indeed one of the options, it means that I previously confirmed the right formulation.

Let’s recap the options carefully. Since we established that the height function is:

\[
h(t) = -16t^2 + 4.8t
\]

It appears the exact formulation given in the options was influenced by gravitational constants or possible input errors:

1. \( h(t) = -12 \cdot 9.8t^2 + 4.8t \)
2. \( h(t) = -\frac{1}{2} \times 9.8 t^2 + 4.8 t \)
3. \( h(t) = -16t^2 + 4.8t \) **(this is indeed one of the options)**
4. \( h(t) = -12 \cdot 4.8t^2 + 4.8t \)
5. \( h(t) = -\frac{1}{2} \cdot 32t^2 + 4.8t + 4.8 \)

### The Correct Choice:

Among these options, the correct height function representation based on your inquiry is:

**h(t) = −16t² + 4.8t**

This is consistent with the physics of projectile motion in the context provided, and it correctly depicts the upward trajectory of the ball given your initial input values.

If there’s anything else you’d like to clarify or delve into, feel free to ask!