When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and, thus, slows him down. Suppose the weight of the sky diver is 914 N and the drag force has a magnitude of 1120 N. The mass of the sky diver is 93.3 kg. What are the magnitude and direction of his acceleration?
magnitude 1 m/s2
direction
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To find the magnitude of the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Weight of the skydiver = 914 N
Drag force = 1120 N
Mass of the skydiver = 93.3 kg
We know that weight is the force due to gravity acting on an object, and it can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2).
Weight = Mass x Acceleration due to gravity
914 N = 93.3 kg x 9.8 m/s^2
Now let's solve for the acceleration due to gravity:
Acceleration due to gravity = Weight / Mass
Acceleration due to gravity = 914 N / 93.3 kg
Acceleration due to gravity ≈ 9.80 m/s^2
Since the upward drag force is initially greater than the weight of the skydiver, it will slow down the skydiver's downward motion. Therefore, the net force acting on the skydiver is the difference between the drag force and the weight.
Net force = Drag force - Weight
Net force = 1120 N - 914 N
Net force ≈ 206 N
Using Newton's second law of motion, we can now find the magnitude of the acceleration:
Net force = Mass x Acceleration
206 N = 93.3 kg x Acceleration
Solving for the acceleration:
Acceleration = Net force / Mass
Acceleration ≈ 206 N / 93.3 kg
Acceleration ≈ 2.21 m/s^2
Therefore, the magnitude of the skydiver's acceleration is approximately 2.21 m/s^2.
As for the direction of the acceleration, it is in the opposite direction of the net force, which is the direction of the drag force acting on the skydiver. In this case, the drag force is directed upward, so the acceleration is directed downward.