The falling stone is a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. The height that it was dropped is 32 feet. The equation for the answer is; <span>16<span>t2</span>+<span>h0</span>=230</span>
<span>−16(t+3<span>)2</span>+<span>h0</span>=14</span>
A falling object has the following height function due to acceleration of gravity (32 ft/s^2)
<span>h(t)=−16<span>t2</span>+<span>v0</span>t+<span>h0 </span></span>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
<span>−16<span>t2</span>+<span>h0</span>=230</span>
<span><span>−16(t+3<span>)2</span>+<span>h0</span>=14</span></span>
