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 869 N and the drag force has a magnitude of 1096 N. The mass of the sky diver is 88.7 kg. Take upward to be the positive direction. What is his acceleration, including sign?
To determine the acceleration of the skydiver, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
Net force = mass × acceleration
In this case, we have two forces acting on the skydiver: weight (downward) and drag force (upward). Since upward is taken as the positive direction, we can write the equation as:
Drag force - Weight = mass × acceleration
Now, let's substitute the given values into the equation.
Drag force = 1096 N (upward)
Weight = 869 N (downward)
Mass = 88.7 kg
1096 N - 869 N = 88.7 kg × acceleration
Simplifying the equation:
227 N = 88.7 kg × acceleration
Now, let's solve for acceleration:
acceleration = 227 N / 88.7 kg
acceleration ≈ 2.56 m/s^2
Therefore, the skydiver's acceleration, including its sign, is approximately 2.56 m/s^2 upward.
To find the acceleration of the skydiver, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
We know that the drag force (the upward force) acting on the skydiver is greater than his weight (the downward force), so the net force will be the difference between these two forces.
Net force = drag force - weight
Given:
Drag force = 1096 N (upward force)
Weight = 869 N (downward force)
Mass = 88.7 kg
Substituting the given values into the equation, we get:
Net force = 1096 N - 869 N
Net force = 227 N (upward force)
Now we can calculate the acceleration using Newton's second law:
Net force = mass * acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Net force / mass
Substituting the values:
Acceleration = 227 N / 88.7 kg
Calculating the value:
Acceleration ≈ 2.56 m/s²
The skydiver's acceleration is approximately 2.56 m/s² in the upward direction.