Question 217218
A projectile is fired directly upward with a muzzle velocity of 860 feet per
 second from a height of 7 feet above the ground.
:
a. Determine a function for the height of the projectile t seconds after it's released.
Assuming the equation: h = -16t^2 + vt + c
h = -16t^2 + 860t + 7
;
b. How long does it take the projectile to reach of height of 100 feet on its way up?
-16^2 + 860t + 7 = 100
-16t^2 + 860t + 7 - 100 = 0
-16t^2 + 860t - 93 = 0
Use the quadratic formulas to find t
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation: x = t: a=-16; b=860; c=-93
{{{t = (-860 +- sqrt( 860^2 - 4 * -16 * -93 ))/(2*-16) }}}
Do the math here and you get: t =.108 seconds for 100' on the way up 
:
c. How long is the projectile in the air?
h = 0, the equation for this -16t^2 + 860t + 7 = 0
Use the quadratic formulas to find t
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation: x = t: a=-16; b=860; c=7
{{{t = (-860 +- sqrt( 860^2 - 4 * -16 * 7 ))/(2*-16) }}}
Do the math here and you get: t = 53.758 seconds to return to earth