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 916 N and the drag force has a magnitude of 1050 N. The mass of the sky diver is 93.5 kg. What are the magnitude and direction of his acceleration?
F = 1050 - 916 = 134 N UP
a = F/m = 134/93.5 = 1.43 m/s^2 UP
in other words his speed down is slowing
To find the magnitude and direction of the skydiver's acceleration, 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. In this case, the net force acting on the skydiver is the difference between the drag force and the weight.
Step 1: Calculate the net force acting on the skydiver
Net force = Drag force - Weight
Net force = 1050 N - 916 N
Net force = 134 N (upward)
Step 2: Calculate the acceleration of the skydiver
Using Newton's second law of motion, we have:
Net force = mass × acceleration
134 N = 93.5 kg × acceleration
To find the acceleration, rearrange the equation:
acceleration = Net force / mass
acceleration = 134 N / 93.5 kg
Step 3: Calculate the magnitude of acceleration
acceleration = 1.43 m/s^2
Step 4: Determine the direction of the acceleration
Since the net force is directed upward and the mass of the skydiver is positive, the acceleration is also directed upward.
Therefore, the magnitude of the skydiver's acceleration is 1.43 m/s^2, and its direction is upward.