I\'ve spent hours on this problem, can not figure it out. Cansomeone please expl

Question

I've spent hours on this problem, can not figure it out. Cansomeone please explain to me how to work this problem. Asimilar problem will be on my exam tomorrow. The solution isin my book, but I don't understand it. I know this is longwith many parts, but I've also posted many short, easy problems aswell and I will rate life saver. thank you.


A stone is thrown from the top of a building with an initialvelocity of 20.0 m/s straight upward, at an initial height of 50.0mabove the ground. The stone just misses the edge of the roofon its way down.
Determine:
a) the time needed for the stone to reach its maximum height
b) the maximum height
c) the time needed for the stone to return to the height from whichit was thrown and the velocity of the stone at that instant
d) the time needed for the stone to reach the ground
e) the velocity and position of the stone at t= 5.00 s.

Given:
coordinate system is y0 = 0 at the level at which thestone is released from the thrower's hand, with y positiveupward.

t = 0, y0 = 0, v0 = 20.0m/s
t = 2.04 s, ymax = 20.4 m, v = 0
t = 4.08 s, y = 0 v = -20.0 m/s
At 50.0m, t = 5.00 s, y = -22.5m, v = -29.0m/s
At the ground, t = 5.83 s, y = -50.0m, v = -29.0m/s

Explanation / Answer

initial velocity v = 20.0 m/s
initial height h = 50.0m (a). Let the time needed for the stone to reach its maximumheight be t then ,       t = v / g where g = 9.8 m / s^ 2 ( b ) . Maximum height reached above initialheight   h is    h ' = v ^ 2 / 2g Maximum height reached above the ground H = h + h' (c). the time needed for the stone to return to the heightfrom which it was thrown and the velocity of the stone at thatinstant be t ' then from the relation    V = u+ gt                                              t= V / g   since initial velocity u = 0 m / s and   V = 200 m / s ( d ) . Let  the time needed for the stone to reachthe ground from maximum height point be t " then     from the relation H = ( 1/ 2) g t " ^2   we find   t " value      Total time of the ball in air T= t + t " substitue values weget answer

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