Question

=
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

$- 16t {}^{2} + 90000 = 0$

$- 16t {}^{2} = - 90000$

$16t {}^{2} = 90000$

$t {}^{2} = \frac{90000}{16}$

$t {}^{2} = 5625$

$t = \sqrt{5625} = + \: or \: - \: 75 \: seconds$

$t = 75 \: seconds$

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