Question

MODELING WITH MATHEMATICS: The function f(t)=-16t^2+10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The same object dropped from the same height on the moon is modeled by g(t)=-8/3t^2+10.

Describe the transformation of the graph of f to obtain g.

The graph of g is a horizontal stretch by a factor of (blank) of the graph of f. Round your answer to the nearest hundredth.

From what height must the object be dropped on the moon so it hits the ground at the same time as on Earth? Round your answer to the nearest hundredth.

The object must be dropped from a height of (blank) feet.

Answer 1

To obtain g from f, the graph of f is horizontally stretched by a factor of 2/3. The object must be dropped from a height of ___ feet.

Step-by-step explanation:

The function f(t)=-16t^2+10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The function g(t)=-8/3t^2+10 models the same object dropped from the same height on the moon.

To obtain g from f, the graph of f is horizontally stretched by a factor of 2/3.

To find the height from which the object must be dropped on the moon to hit the ground at the same time as on Earth, we set g(t) = 0 and solve for t.

Substituting the value of t back into g(t) will give us the height.