a water balloon is tossed into the air with an upward velocity of 25 ft/s. its height h(t) in ft after t seconds is given by the function h(t) = − 16t2 + 25t + 3. show your work.

19. after how many seconds will the balloon hit the ground? (hint: use the quadratic formula)

Given 
h(t)=-16t^2+25t+3
assume h(t) is height measured upwards from ground.
Need h(t)=0 for t>0.
solve
h(t)=-16t^2+25t+3=0
use quadratic formula, A=-16, B=25, C=3
t=(-B +/- sqrt(B^2-4AC))/2A
=-25-sqrt(25^2+192)/(-32)
= {-0.11198, 1.6745} seconds
reject negative root, so
time = 1.6745 seconds.

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