Moments after making the dreaded decision to jump out the door of the airplane flying at 12,944 feet, a skydiver's 84.3-kg body experiences 124 N of air resistance. The magnitude of the skydiver's downward acceleration at this instant in time is ______ m/s2. Use the approximation g ≈ 10 m/s2.
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To find the magnitude of the skydiver's downward acceleration, we need to calculate the net force acting on the skydiver.
The net force is equal to the gravitational force (weight) minus the air resistance:
Net force = Weight - Air resistance
The weight is equal to the mass of the skydiver multiplied by the acceleration due to gravity:
Weight = mass * acceleration due to gravity
Given:
Mass (m) = 84.3 kg
Acceleration due to gravity (g) ≈ 10 m/s²
Air resistance (F_air) = 124 N
Weight = 84.3 kg * 10 m/s²
Weight = 843 N
Now, we can calculate the net force:
Net force = 843 N - 124 N
Net force = 719 N
Finally, we can calculate the magnitude of the skydiver's downward acceleration using Newton's second law:
Net force = mass * acceleration
719 N = 84.3 kg * acceleration
To find acceleration:
acceleration = Net force / mass
acceleration = 719 N / 84.3 kg
Using a calculator, we get:
acceleration ≈ 8.53 m/s²
Therefore, the magnitude of the skydiver's downward acceleration at this instant in time is approximately 8.53 m/s².
To find the magnitude of the skydiver's downward acceleration, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration (F = ma). In this case, the net force is the difference between the force of gravity acting downwards and the force of air resistance acting upwards.
The force of gravity can be calculated using the formula Fg = mg, where m is the mass of the skydiver and g is the acceleration due to gravity (approximated as 10 m/s^2).
Fg = mg
Fg = (84.3 kg)(10 m/s^2)
Fg = 843 N
Now, we can calculate the magnitude of the skydiver's downward acceleration by rearranging Newton's second law equation:
F - Fg = ma
Where:
F is the force of air resistance (124 N)
Fg is the force of gravity (843 N)
m is the mass of the skydiver (84.3 kg)
a is the acceleration
124 N - 843 N = (84.3 kg)a
-719 N = (84.3 kg)a
To find the magnitude of the skydiver's downward acceleration, we divide both sides of the equation by the mass of the skydiver:
a = -719 N / 84.3 kg
a ≈ -8.54 m/s^2
As acceleration is a vector, the negative sign indicates that it is directed upward, opposing the downward motion. Thus, the magnitude of the skydiver's downward acceleration is approximately 8.54 m/s^2.