a frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h(t)=-16t^2+64t+3 what is the height of the natural jump
To find the height of the natural jump, we need to find the maximum height that the frog reaches during its leap.
The height function of the frog is h(t) = -16t^2 + 64t + 3.
To find the maximum height, we need to find the vertex of the parabola defined by this function. The vertex of a parabola in the form y = ax^2 + bx + c is at the point (h, k), where h = -b/(2a) and k = f(h), where f(h) = ah^2 + bh + c.
In this case, a = -16, b = 64, and c = 3:
h = -b/(2a) = -64/(2*-16) = -64/-32 = 2
k = f(2) = -16(2)^2 + 64(2) + 3 = -16(4) + 128 + 3 = -64 + 128 + 3 = 67
Therefore, the maximum height the frog reaches during its leap is 67 feet.