A student designs a container to prevent an egg from breaking when dropped from a height of 30 feet. Write a function that gives the height h (in feet) of the container after t seconds.

As i understand, you put an egg inside a container, and then you drop it from 30ft above the ground.

Now, when the container is in the air, the only force acting on it will be the gravitational force (we can discard things like the air resistance, as we do not know the shape or volume of the container).

The gravitational acceleration is g = 32.2ft/s^2

Then the acceleration of the container will be:

A(t) = -32.2ft/s^2

For the velocity, we need to integrate over time to get:

V(t) = (-32.2ft/s^2)*t + v0

where v0 is the initial velocity, as the container is "dropped", the initial velocity is zero, then:

V(t) = (-32.2ft/s^2)*t

For the position, or height in this case, we integrate again over time, and get:

P(t) = (1/2)*(-32.2ft/s^2)*t^2 + p0

Where p0 is the initial height, 30 ft in this case.

Then the equation for the height, as a function of time, is:

P(t) = (-16.1ft/s^2)*t^2 + 30ft.

Where the fact that the container is made in such a way that an egg inside of it does not break (For example, made of a really dense and elastic material that can absorb all the energy of the impact), does not change anything in this equation, as the kinematics do not depend on that kind of properties.

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step-by-step explanation: