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(t) = -16t² + 4. The distance in feet traveled by an object at a constant speed of 20 feet per second is given by d(t) = 20t. These two functions can be combined to build a new function, f, that models the height of the volleyball as a function of time in t seconds. Which choice shows how to combine h and d to build f?

1) f(t) = h(t) + d(t)
2) f(t) = h(t) - d(t)
3) f(t) = h(t) * d(t)
4) f(t) = h(t) / d(t)

Answer 1

To model the height of a volleyball as a function of time, the correct choice is option 1, f(t) = h(t) + d(t), where h(t) represents the height affected by gravity and d(t) accounts for horizontal distance traveled, which is not necessary for this model.

Step-by-step explanation:

The student is asking how to combine two functions to model the height of a volleyball over time when it is hit upwards.

Function h(t) represents the height of the ball due to gravity, while d(t) represents the distance traveled by the ball at a constant speed. Since d(t) describes horizontal motion that is irrelevant when calculating the vertical height of a ball, we only need to focus on h(t) to model the vertical height.

Thus, the correct choice to model the height of a volleyball as a function of time in t seconds is choice 1, which is f(t) = h(t) + d(t), although technically the d(t) term is not needed and could be omitted as it is unrelated to the height.