acceleration downward due to gravity is 10m/s to be exact 9.8m/s
this is enough to get you to start thinking
h(t) = -4.9t^2 + 30t + 53
a) ball goes up, comes back down to the top of the tower. So, we want
53 = -4.9t^2 + 30t + 53
0 = -4.9t^2 + 30t
0 = t(-4.9t + 30)
so, t=0 (at the start) or t = 6.12 (as it comes back down)
If t(-4.9t+30)=0, either
-4.9t+30 = 0
That is, t = 6.12
If you can't solve a factored expression, you have some review to do.
b) same calculation but, t is between 0 and 6.12. That is 0 < t < 6.12
c) same calculation, but restricting t to positive values, t>6.12
Naturally, we could also restrict t to the point where height >= 0.
d) vertex of any parabola is where x = -b/2a = -30/-9.8 = 3.06
you know from the quadratic formula that x = -b/2a ± sqrt(blah blah)
Parabolas are symmetric, so the vertex is midway between the roots, which are equally spaced around x = -b/2a
h(3.06) = 98.9
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