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Homework Statement
Bungee Man is a superhero who does super deeds with the help of Super Bungee cords. The Super Bungee cords act like ideal springs no matter how much they are stretched. One day, Bungee Man stopped a school bus that had lost its brakes by hooking one end of a Super Bungee to the rear of the bus as it passed him, planting his feet, and holding on to the other end of the Super Bungee until the bus came to a halt. (Of course, he then had to quickly release the Super Bungee before the bus came flying back at him.) The mass of the bus, including passengers, was 1.20×104 kg, and its speed was 21.2 m/s. The bus came to a stop in 50.0 m.
B) How much time after the Super Bungee was attached did it take the bus to stop?
x = 50 m
m = 1.20x104 kg
v = 21.2
k = 2160 N/m (calculated in Part A of the question. I used the conservation of energy to figure it out)
Homework Equations
T = 2pi x sqrt(k/m)
v = -Awsin(wt)
x = Acos((2pi/T) x t)
The Attempt at a Solution
I solved this problem by finding the period T, and dividing this by 2, since the point at which the bus stops would be equal to half of the period in SHM. Now I'm starting to wonder whether the initial velocity of the bus would cause the bus to actually take longer than T/2 to reach that point where it stops. I even tried using simple kinematics to solve this problem, but that didn't work either. For T, I got 14.8, and divided it by 2 to get 7.40, which is wrong...does anyone know what I'm doing wrong?