To answer both questions, we can use Newton's second law of motion, which states:
F = m * a
where F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object.
Question 1:
We are given the force acting on the torso, F = 260,000 N, and the mass of the torso, m = 3800 kg. We need to find the upward acceleration (a) of the torso.
Using Newton's second law, we have:
260,000 N = 3800 kg * a
Dividing both sides by 3800 kg:
a = 260000 N / 3800 kg
a = 68.42 m/s^2
Therefore, the magnitude of the torso's upward acceleration as it comes to rest is 68.42 m/s^2.
Question 2:
We are given the distance the torso falls, d = 1.21 m. We need to find the time required for the torso to come to rest once it contacts the ground.
To find the time (t), we can use the kinematic equation:
d = (1/2) * a * t^2
Rearranging the equation:
t^2 = (2 * d) / a
Substituting the values, we can solve for t:
t^2 = (2 * 1.21 m) / 68.42 m/s^2
t^2 = 0.035298 s^2
Taking the square root of both sides:
t = sqrt(0.035298 s^2)
t ≈ 0.188 s
Therefore, it takes approximately 0.188 seconds for the torso to come to rest once it contacts the ground.