Question

Last Sunday Luca jumped into the foam zone at Sky Zone. His height as a funetion of time can be modeled by the function AI) -

- 16f4 16t + 10, where tis the
time in seconds and h in the height in feet.
a.) How long did it take for Luca to reach his maximum height?
b.) What was the highest point that Luca reached?

Answer 1

Answer: Luca’s height as a function of time can be modeled by the equation:

h(t) = -16t^2 + 16t + 10

where h is the height in feet and t is the time in seconds.

a) To find the time it took for Luca to reach his maximum height, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

t = -b / 2a

where a = -16 and b = 16. Substituting these values, we get:

t = -16 / 2(-16) = 0.5

Therefore, it took Luca 0.5 seconds to reach his maximum height.

b) To find the highest point that Luca reached, we need to find the maximum value of the function. The maximum value occurs at the vertex of the parabola. We already know that the x-coordinate of the vertex is 0.5 seconds. To find the y-coordinate, we substitute t = 0.5 into the equation:

h(0.5) = -16(0.5)^2 + 16(0.5) + 10 = 18 feet

Therefore, Luca reached a height of 18 feet.

Explanation: