Question

A volleyball is hit upward from a height of 4 feet at an initial speed of 20 feet per second. As the volleyball travels, Earth’s gravity slows it down. The height of an object dropped from a height of 4 feet is given by ℎ()=−16^2+4. The distance in feet traveled by an object at a constant speed of 20 feet per second is given by ()=20. These two functions can be combined to build a new function, , that models the height of the volleyball as a function of time in seconds.

Which choice shows how to combine ℎ and to build ?

A) ()=ℎ()−() ()=−162−20+4
B) ()=()−ℎ() ()=162+20−4
C) ()=ℎ()·() ()=(−162+4)(20)
D) ()=ℎ()+() ()=−162+20+4

Answer 1

To combine the two given functions, set h(t) = 0 to find the time it takes for the volleyball to reach the ground, and then substitute this value into the function d(t) to find the distance traveled at a constant speed of 20 feet per second.

Step-by-step explanation:

The function that models the height of the volleyball as a function of time in seconds can be built by combining the two given functions, h(t) = -16t^2 + 4 and d(t) = 20.

In order to combine the two functions, we need to find the time it takes for the volleyball to reach the ground. We can do this by setting h(t) = 0 and solving for t. By substituting this value of t into the function d(t), we can find the distance traveled by the volleyball at a constant speed of 20 feet per second.

The correct choice to combine h(t) and d(t) is A) h(t) - d(t), which gives us the function h(t) = -16t^2 + 4 - 20.