A flare is launched from a boat. The height, h, in meters, of the flare above the water is approximately modelled by the function h(t) = -15t2 + 150t, where t is the number of seconds after the flare is launched. How many seconds will it take for the flare to return to the water?
To find when the flare returns to the water, we need to find when the height above the water is equal to zero.
Setting h(t) = 0, we get:
-15t^2 + 150t = 0
Factoring out a t, we get:
t(-15t + 150) = 0
Setting each factor to zero:
t = 0 and -15t + 150 = 0
-15t = -150
t = 10
So, the flare will return to the water after 10 seconds.