Question

Luca is in a culvert below street level. He launches an object at an upward velocity of 40 feet per second. Use GeoGebra to graph the situation using the formula y=−16t2+40t−5
. How far above or below street level is Luca’s initial launching point?(1 point)
Responses

5 feet above
5 feet above

5 feet below
5 feet below

0 feet above or below
0 feet above or below

2.5 feet below

Answer 1

To determine how far above or below street level Luca's initial launching point is, we need to analyze the given equation:

\[ y = -16t^2 + 40t - 5 \]

Here, \( y \) represents the height of the object above or below street level at time \( t \), and the constant term \(-5\) indicates the initial position of the object in vertical units compared to the street level.

Since the equation starts with \(-5\), it means that at time \( t = 0 \) (the moment of launch), the initial height \( y(0) \) can be calculated as:

\[ y(0) = -16(0)^2 + 40(0) - 5 = -5 \]

This shows that Luca’s initial launching point is 5 feet below street level.

Therefore, the correct response is:

**5 feet below**.