1)
h(t) = -4.9*t^2 + 29.4*t + 1
differentiate with t to get velocity,
h’(t) = d/dt(h(t))
= d/dt(-4.9*t^2 + 29.4*t + 1)
= -4.9*2*t + 29.4
= -9.8t + 29.4
At maximum height, velocity is 0
so,
-9.8t + 29.4 = 0
t = 3.0 s
Answer: 3.0 s
2)
Lets find the height at this time
h(t) = -4.9*t^2 + 29.4*t + 1
at t=3.0 s,
h(3.0) = -4.9*(3.0)^2 + 29.4*(3.0) + 1
= -44.1 + 88.2 + 1
= 45.1 m
Answer: 45.1 m
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