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. What is the highest point that the flare reaches?
To find the highest point that the flare reaches, we need to find the maximum value of the function h(t)=-15t^2 + 150t.
To do this, we first need to find the vertex of the parabolic function. The vertex of a parabolic function of the form h(t) = at^2 + bt + c is given by the formula t = -b/2a.
In this case, a = -15 and b = 150, so the vertex of the function h(t) is at t = -150/(2*(-15)) = -150/-30 = 5 seconds.
To find the maximum height reached by the flare, we substitute t = 5 into the function h(t):
h(5) = -15(5)^2 + 150(5) = -15(25) + 750 = -375 + 750 = 375
Therefore, the highest point that the flare reaches is 375 meters above the water.