Question

In an engineering class, students are challenged to design a container that prevents an egg from breaking when dropped from a height of 50 feet. The formula that models this is
h(t)=-16ft^2+50


where h(t) is the final height, t is the time in seconds. It hits the ground when the final height is zero. How long does it for the egg to hit the ground. Round to the nearest hundredth

Answer 1

For the given formula to represents the height h(t) of the egg dropped in time 't' seconds  is h(t) = -16t² + 50 then the time required by the egg to hit the ground is equal to 1.77 seconds ( round off to the nearest hundredth).

As given in the question,

Given formula to represents the height 'h(t)' of the egg to be dropped in time 't' seconds is given by :

h(t) = -16t² + 50

Condition given :

Egg hits the ground when final h(t) is equal to 0.

0 = -16t² + 50

⇒ 16t² = 50

⇒ t² = 50 / 16

⇒ t² = 3.125

⇒ t = √3.125

⇒ t = 1.7677..

⇒ t = 1.77 seconds

Therefore, for the given formula to represents the height h(t) of the egg dropped in time 't' seconds  is h(t) = -16t² + 50 then the time required by the egg to hit the ground is equal to 1.77 seconds ( round off to the nearest hundredth).

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