import numpy as np import matplotlib.pyplot as plt

#Use this cell to calculate the velocity of a ball after falling 2 meters initialHeight = 2 # meters gravityAccMag = 9.81 #meters/s^2, magnitude of acceleration due to gravity ##### Begin Editing ##### finalVelocity = (2 * gravityAccMag * initialHeight) ** 0.5 # in meters/s. This should be a vector. ##### End Editing ##### velocityMagnitude = np.linalg.norm(finalVelocity) #numpy.linalg.norm takes the magnitude of an array print('The final velocity of a ball after falling 2 meters has a magnitude of {} meters/second'.format(velocityMagnitude))

#Use this cell to calculate the magnitude of the drag force for a ball that has fallen 2 meters vel = velocityMagnitude*np.array([1./np.sqrt(3),1./np.sqrt(6),1./np.sqrt(2)]) # meters/s r = 0.025 # meters ##### Begin Editing ##### A = np.pi * r**2 #m^2 C = 0.5 #unitless rho = 1.225 #kg/m^3 dragForce = -0.5 * C * A * rho * np.linalg.norm(vel)**2 ##### End Editing ##### dragMagnitude = np.linalg.norm(dragForce) print('The magnitude of the air drag force is {}'.format(dragMagnitude))

#Run this cell without editing print(np.linalg.norm(vel)*vel) print(vel*vel)

#Use this cell to calculate the ratio of the magnitude of the drag force to gravity ##### Begin Editing ##### mass_ball_g = 75 g = 9.81 mass_ball_kg = mass_ball_g / 1000 gravityForce = mass_ball_kg * np.array([0, 0, -g]) ##### End Editing ##### gravityMagnitude = np.linalg.norm(gravityForce) ratio = dragMagnitude / gravityMagnitude print('The ratio of the air drag force to gravity is {}'.format(ratio))