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 = −16t^2 + 40t − 5. How far above or below street level is Luca’s initial launching point?

Question

A) 5 feet below
B) 2.5 feet below
C) 0 feet above or above
D) 5 feet above

Answer 1

To find out how far above or below street level Luca's initial launching point is, we need to evaluate the quadratic equation given:

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

In this equation, \( y \) represents the height of the object at time \( t \), and the constant term \(-5\) represents the initial height of the launching point relative to street level.

The constant \(-5\) implies the height at \( t = 0\):

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

This means that at the moment of the launch (when \( t = 0 \)), the object's position is \( -5 \) feet. This indicates that Luca's initial launching point is 5 feet below street level.

Thus, the answer is:

A) 5 feet below