Question

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If an object were to fall from a
height of 90,000 feet in the air, and
the equation for height as a
function of time is:
y = -16t2 + 90,000
where t is time in seconds and y is height
in feet, how many seconds will it take for
the object to hit the ground?
Set the equation equal to zero and solve.
t = [ ? ] seconds

Answer 1

We want to determine when it's height is equal to zero:

Set y=0

`- 16t {}^(2) + 90000 = 0`

`- 16t {}^(2) = - 90000`

`16t {}^(2) = 90000`

`t {}^(2) = (90000)/(16)`

`t {}^(2) = 5625`

`t = √(5625) = + \: or \: - \: 75 \: seconds`

`t = 75 \: seconds`

The negative time is rejected. As we cannot have a negative value.