Asmall rock falling from the top of a 124-ft-tall building with an initial downward velocity of –30 ft/sec is modeled by the equation h(t) = –16t2 – 30t + 124, where t is the time in seconds. for which interval of time does the rock remain in the air?

2 second

Explanation:

The time taken by rock in air is calculated by putting h(t) = 0. It is because as it strikes the ground, height is zero.

Now put h(t) = 0

Use quadratic formula

Taking positive sign, as time cannot be negative

t = 2 second

Explanation:

It is given that,

The equation of the motion of a small rock as a function of time t is given by :

.............(1)

We need to find the time interval for which the rock remain in the air. It can be solved by equating, h(t) = 0

On solving the above quadratic equation, we get the value of t as :

and

As the value of t is positive always, so, the interval for which the rock remain in the air is :

Hence, this is the required solution.

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