Question

A bird drops a stick from a height of 52 ft. The function h=-16t^2+52 gives the sticks approximate height h above the ground, in feet, after the seconds. Graph the function. About what time does the stick hit the ground?use inequalities to describe a reasonable domain and range for the function.

Answer 1

Explanation:

To graph the function h = -16t^2 + 52, we can create a table of values and plot the points:

t h

0 52

0.5 42

1 36

1.5 34

2 36

2.5 42

3 52

Then we can plot these points on a coordinate system to get the graph of the function:

Graph of h = -16t^2 + 52

To find the time at which the stick hits the ground, we need to set h = 0 and solve for t:

0 = -16t^2 + 52

16t^2 = 52

t^2 = 3.25

t = ±√3.25

Since time cannot be negative in this context, we take the positive value:

t ≈ 1.8 seconds

Therefore, the stick hits the ground after approximately 1.8 seconds.

To describe a reasonable domain and range for the function, we need to consider the context of the problem. Since the height of the stick is measured in feet, we can assume that t represents time in seconds. In this case, a reasonable domain for the function would be t ≥ 0, since time cannot be negative. For the range, we can see from the graph that the maximum height of the stick is 52 feet, and the minimum height is 0 feet (when the stick hits the ground). Therefore, a reasonable range for the function would be 0 ≤ h ≤ 52.