create python code to figure out start velocity

November 3, 2023

Have a task and need to figure out the start velocity of an iron ball shot vertically upwards. We know this information.

>Solution :

The values from your image are as follows:

mass sphere: 263.8602726 kg
drag coefficient: 0.47
air density: 1.225 kg/m³
max height: 80 m
acceleration due to gravity (G): 9.805 m/s²

Assuming you can neglect air resistance, you could use the kinematic equation:

v^2 + u^2 = 2as

where:

v is the final velocity (0 m/s at the maximum height).
u is the start velocity.
a is the acceleration (in this case, -9.805 m/s² due to gravity).
s is the displacement (80 m).

We can rearrange the equation to solve for the start velocity u:

u = sqrt(v^2 -2as)

Implementing this in Python is relatively straightforward:

def calculate_start_velocity(displacement: float,
                             acceleration: float) -> float:
  """Calculate the start velocity for an object given its displacement and acceleration.

  Args:
      displacement: The displacement of the object (maximum height reached).
      acceleration: The acceleration (should be negative for gravity).

  Returns:
      float: The calculated start velocity.
  """
  final_velocity_squared = 0  # Since final velocity at max height is 0.
  start_velocity_squared = final_velocity_squared - 2 * acceleration * displacement
  start_velocity = start_velocity_squared**0.5
  return start_velocity


def main() -> None:
  """Main function to calculate and print the start velocity."""
  max_height = 80.0  # Displacement.
  gravity = -9.805  # Acceleration due to gravity.
  start_velocity = calculate_start_velocity(max_height, gravity)
  print(f'The start velocity is: {start_velocity:.2f} m/s')


if __name__ == '__main__':
  main()

Output: