A ball is thrown downward from a window in a tall building. Its position in time t in seconds is s=16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the ball to fall 206 feet?

we know from 2nd eqn of motion that

s= ut +0.5at2

and given is s=32t+16t2

equating the coefficients, we get u=initial veloctiy =32ft/s  &  a=acceleartion=32ft/s2

time taken to fall 206 ft =,we solve for t:

206=32t+16t2

16t2+32t-206=0

t={-32+sqrt(1024+13184)}/32 =-1+3.72= 2.72 seconds = 2.7 seconds =answer

or

t=={-32-sqrt(1024+13184)}/32= -1-3.72 <0   time cant be negative