Question 193178
An object that is projected straight downward with initial velocity of v feet per second is at a height from ground {{{ h=-16t^2-vt+s }}} , where s = initial height in feet, and t = time in seconds. If Bianca is standing on a ledge 46.75 feet above the ground and throws a penny straight down with an initial velocity of 12 feet per second, in how many seconds will it reach the ground?
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{{{ h=-16t^2-vt+s }}}
The problem gives you:
s (initial height) as 46.75 feet
v (initial velocity) as 12 feet/sec
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Since they want to know when it will reach the ground -- h (height) would be 0.
So, set h = 0 and solve for 't':
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{{{ h=-16t^2-vt+s }}}
{{{ 0=-16t^2-12t+46.75 }}}
Since we can't factor, use the quadratic equation to solve.  Doing so yields:
t={-2.125, 1.375}
Throw out the negative solution -- this leaves:
t = 1.375 seconds
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Details of quadratic follows:
*[invoke quadratic "t", -16, -12, 46.75 ]