Question

a falling stone is at a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. From what height was it dropped?

Answer 1

a falling object has the following height function due to acceleration of gravity (32 ft/s^2)
\[h(t) = -16t^{2} + v_0 t + h_0\]

Answer 2

since object was dropped assume initial velocity of 0
plug in 2 given points to obtain system of 2 equations
solve for t and initial height
\[-16t^{2} +h_0 = 230\]
\[-16(t+3)^{2}+h_0 = 14\]