Answer:
Maximum height reached = -602.1 feet
Step-by-step explanation:
Maximum height is attained at final velocity, v = 0 feet per second
Initial velocity, u = 101 feet(ft) per second(s) = 101ft/s (given)
Assume acceleration due to gravity, g = [tex]10m/s^{2}[/tex]
Using the first equation of motion, v = u + at
a = -g since the rollercoaster is moving upwards (-) and will be under the influence of gravity g.
Therefore, v = u - gt
v + gt = u
gt = u - v
Divide both sides by g
[tex]\frac{gt}{g} =\frac{u-v}{g}\\ \\t = \frac{101-0}{10} = \frac{101}{10}\\\\t = 10.1 seconds[/tex]
At t = 10.1s, a maximum height will be reached
[tex]h(10.1s) = -16(10.1^{2}) + 101(10.1) + 10\\ \\h(10.1s) = -16(102.01) + 1020.1 + 10 = -1632.16 + 1030.1\\\\h(10.1s) = -602.06ft[/tex]
h(10.1s) ≅ -602.1 ft
