the object will hit the ground when P(t) = 0, for some t, and t > 0

P(t)= −16 (t)^2+339(t)

P(t)= 0

−16 (t)^2+339(t) = 0

by solving the quadratic equation we find

t = 339/16 s

t = 21.19 s

click here to see the step by step solution of the equation

the object will hit the ground after 21.19 seconds.