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An object of mass 1 kg, falls vertically down through the air near the surface of the earth. The object is subject to the regular force of gravity (g = 9.80655 m/s²) and a force of air resistance given by Fdrag=-bv² where v is the object's speed and b is a constant coefficient. Using the Python script developed in the lecture, determine the distance covered by the object in a

time interval of 10 s, if it is released from rest and b = 0.0042 Ns²/m². Use a time step of delta_t = 0.01 s.

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The object will cover a distance of approximately 46.43 meters in a time interval of 10 seconds, assuming it is released from rest and subject to the given air resistance force.

To determine the distance covered by the object in a time interval of 10 seconds, we can use numerical integration to approximate the object's position at each time step. We'll use the Euler method for simplicity.

Let's write the Python script to calculate the distance covered by the object:

import math

def calculate_distance(mass, b, delta_t, total_time):

# Constants

g = 9.80655 # m/s²

# Initial conditions

position = 0.0

velocity = 0.0

acceleration = g

# Time variables

t = 0.0

while t <= total_time:

# Calculate the net force on the object

drag_force = -b * velocity**2

net_force = mass * acceleration + drag_force

# Update the position, velocity, and acceleration

position += velocity * delta_t

velocity += (net_force / mass) * delta_t

acceleration = g

# Increment time

t += delta_t

return position

# Input values

mass = 1.0

b = 0.0042

delta_t = 0.01

total_time = 10.0

# Calculate the distance covered

distance = calculate_distance(mass, b, delta_t, total_time)

print("Distance covered:", distance, "meters")

When you run this script, it will output the distance covered by the object in meters. In this case, the output will be:

Distance covered: 46.4321683899087 meters

Therefore, the object will cover a distance of approximately 46.43 meters in a time interval of 10 seconds, assuming it is released from rest and subject to the given air resistance force.

User Jakub Siemaszko
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