SOLUTION: A rock is thrown upward from a bridge into a river below. The function f(t)=-16t^2+38t+90 determines the height of the rock above the surface of the water (in feet) in terms of the

Question 1125996: A rock is thrown upward from a bridge into a river below. The function f(t)=-16t^2+38t+90 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.
a. What is the bridge's height above the water?
b. How many seconds after being thrown does the rock hit the water?
c. How many seconds after being thrown does the rock reach its maximum height above the water?
d. What is the rock's maximum height above the water?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The height is 90 feet, the constant in the equation
maximum height is where t=-b/2a of the quadratic or -38/-32 or t=19/16 sec
putting that into the equation, height max is 112.6 feet
set it equal to 0 to find the landing time
16t^2-38t-90=0, rewriting with positive first term
t=(1/32)(38+/- sqrt (1444+5760)0; sqrt 7200=84.85
t=3.84 sec until it hits the water

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