Suppose Jessica drops a rock from a hot air balloon 200m above the water. how long does it take the rock to fall (a) the first 100 meters and (b) the second 100 meters?
a. 0.5g*t^2 = 100. 4.9t^2 = 100, t = 4.52 s.
b. V = Vo + g*t = 0 + 9.8*4.52 = 44.3 m/s. = Velocity after falling 100 m.
Vo*t + 0.5g*t^2 = 100.
44.3*t + 0.5g*t^2 = 100,
4.9t^2 + 44.3t - 100 = 0,
Use Quadratic formula:
t = (-B+-sqrt(B^2-4AC)/2A.
t =(-44.3+-sqrt(44.3^2+1960)/9.8,
t = (-44.3 +- 62.63)/9.8 = 1.87 and -10.9 s.
Solution: t = 1.87 s.