A paratrooper with a fully loaded pack has a mass of 119 kg. The force due to air resistance on him when falling with an unopened parachute has magnitude FD = bv^2 where b = 0.13 (N·s^2)/m^2.
The force of air resistance acting on him is 516N up.
(b) What is his acceleration?
To find the acceleration of the paratrooper, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
In this case, we know the force due to air resistance is 516 N and it acts upward. Since the force acting on the paratrooper is opposite to the direction of motion (downward), we will consider it negative. Therefore, the equation becomes:
-516 N = 119 kg * a
Now, let's solve for the acceleration (a):
a = (-516 N) / 119 kg
a ≈ -4.33 m/s²
Therefore, the acceleration of the paratrooper is approximately -4.33 m/s². Note that the negative sign indicates that the acceleration is directed opposite to the initial motion.