Lesson Physics as Gravity (Mathematical)
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Notice: This is when you throw an object vertically. Equation to notice: {{{f(t) = -16t^2 + vt + h}}} where {{{t}}} is time .. {{{v}}} is initial velocity ..{{{h}}} is the height above the ground .. {{{f(t)}}} is the height after {{{t}}} seconds Example: I toss a 5 pound ball vertically at an initial rate of 32 meters per second from the top of a water tower that is 10 meters tall. v = 32 h = 10 {{{f(t) = -16t^2 + 32t + 10}}} When will the ball hit the ground? {{{0 = -16t^2 + 32t + 10}}} {{{0 = -8t^2 + 16t + 5}}} {{{t = (-b +- sqrt(b^2 - 4ac))/(2a)}}} {{{t = (-16 +- sqrt(16^2 - 4(-8)(5)))/(2(-8))}}} {{{t = (-16 +- sqrt( 256 + 160 ))/(-16)}}} {{{t = (-16 +- sqrt(416))/(-16)}}} {{{t = 1 +- sqrt(416)/(-16)}}} Look at the positive time: {{{t = 1 - sqrt(416)/(-16)}}} The ball would hit the ground after about 2.2748 seconds. What is the maximum height the ball would reach, and when is that? Vertex: ((-b/2a),f(x)) = (1,26) After one second, the ball will reach its max height: 26 meters ....
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