Question

For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 60 ft. The function is modeled by h(t)=−16t^2+60. How long does it take for the container to hit the ground?

Answer 1

To determine the time it takes for the egg's container to hit the ground from 60 ft, the quadratic function h(t) = -16t^2 + 60 is set to zero, and by solving for t, we find it takes approximately 1.94 seconds.

Step-by-step explanation:

For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 60 ft. To determine how long it takes for the container to hit the ground, we can use the quadratic function h(t) = -16t2 + 60, which models the height of the container above the ground as a function of time. In this scenario, hitting the ground corresponds to the height h(t) being zero. To find the time it takes for the container to hit the ground, we set the equation equal to zero and solve for t:
0 = -16t2 + 60

Divide both sides by -16 for simplicity:
0 = t2 - (60/16)
0 = t2 - 3.75

To solve this quadratic equation, we take the square root of both sides, remembering that we only consider the positive root because time cannot be negative:
t = √3.75
t ≈ 1.9365 seconds

Thus, it takes approximately 1.94 seconds for the container to reach the ground.