Question 423045
An object is launched straight up into the air at an initial velocity of 64 feet per second.
 It is launched from 6 feet off the ground.
 Its height H, in feet, at t seconds is given by the equation H=-16tē+64t+6.
 Find all times t that the object is at a height of 54 feet off the ground.
:
H = 54
therefore:
-16tē + 64t + 6 = 54
-16t^2 + 64t + 6 - 54 = 0
-16t^2 + 64t - 48 = 0
Simplify, divide thru by -16; results:
t^2 - 4t + 3 = 0
Factor
(t - 3)(t - 1) = 0
Two solutions
t = 1 sec, 54 ft on the way up
and
t = 3 sec, 54 ft on the way down
:
{{{ graph( 300, 200, -2, 6, -50, 100, -16x^2 + 64x + 6, 54)  }}}
green line is at 54 ft