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?
ma=F(fr)-W,
a= (F(fr)-W)/m = (1120-914)/93.3 = 2.2 m/s² (upwards)
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 applied to an object is equal to the mass of the object multiplied by its acceleration.
First, we need to calculate the net force acting on the skydiver. The net force is the difference between the drag force and the weight of the skydiver. The weight can be calculated by multiplying the mass of the skydiver by the acceleration due to gravity (which is approximately 9.8 m/s^2).
Weight of the skydiver = mass * acceleration due to gravity
Weight = 93.3 kg * 9.8 m/s^2 = 914.34 N (approximately)
Now we can calculate the net force:
Net force = Drag force - Weight
Net force = 1120 N - 914.34 N
Net force = 205.66 N (approximately)
With the net force calculated, we can now calculate the acceleration using Newton's second law:
Net force = mass * acceleration
205.66 N = 93.3 kg * acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Net force / mass
Acceleration = 205.66 N / 93.3 kg
Acceleration = 2.205 m/s^2 (approximately)
The magnitude of the skydiver's acceleration is approximately 2.205 m/s^2.
To determine the direction of the acceleration, we look at the forces acting on the skydiver. In this case, the drag force is acting in the upward direction (opposite to the force of gravity), so the acceleration will also be in the upward direction.
Therefore, the magnitude of the skydiver's acceleration is approximately 2.205 m/s^2, and the direction is upward.