<span>Your equation for the height of the stone at any time is h(t) = -16t2<span> + 128t + 32 .
From your equation, we can tell that you're defining the upward direction as positive. We can also tell that you threw the stone upward, with an initial speed as it left your hand of 128 feet per second, about 87 miles per hour ... a mighty toss indeed, and I think there's a man from the Chicago Cubs waiting outside who'd like to talk to you.
Anyway, When the stone splashes into the water, h(t) = 0 . </span></span> <span>-16t²<span> + 128t + 32 = 0</span></span>
Divide each side by -16 :
t² - 8t - 2 = 0
I don't see any easy way to factor the expression on the left, so I have to use the quadratic formula to solve this equation.
t = 4 plus and minus √18 .
t = +8.24 seconds t = -0.24 second
Mathematically, both numbers are valid solutions.But when you apply the equation to a real world situation, only the positive 't' makes sense. So <u> t = 8.24 seconds</u>.
The Kinetic energy which was exerted and experience pulling the string of a bow is kept as a potential energy at the end of the arrow in contact with the string. Once release from aim at stationary position the potential energy is again transformed.
