Question
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?
Answers
Henry
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.
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.