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.
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
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