import math
#Given that
F = [2.5,4.5,-5] # F is a force vector act through origin
F_magnitude = math.sqrt ( 2.5**2 + 4.5**2 + (-5)**2)
theta1_x = (180 / pi ) * math.acos ( 2.5 / F_magnitude)
theta1_y = (180 / pi ) * math.acos ( 4.5 / F_magnitude)
theta1_z = (180 / pi ) * math.acos ( -5 / F_magnitude)
print " Magnitude of force F is ",round(F_magnitude,4)," N"
print " Angle made with X - axis is ",round(theta1_x,4)," degree"
print " Angle made with Y - axis is ",round(theta1_y,4)," degree"
print " Angle made with Z - axis is ",round(theta1_z,4)," degree"
import math
#Given that
r = [2,2,2*math.sqrt(2)]
r_magnitude = math.sqrt ( 2**2 + 2**2 + (2*math.sqrt(2))**2)
math.cos_x = ( 2 / r_magnitude)
math.cos_y = ( 2 / r_magnitude)
math.cos_z = ( 2.8284 / r_magnitude)
print " Directional math.comath.sine in X - axis is ",math.cos_x," "
print " Directional math.comath.sine in Y - axis is ",math.cos_y," "
print " Directional math.comath.sine in Z - axis is ",math.cos_z," "
import math
#Given that
r_xz = [2,2.8282]
r_xz = math.sqrt (2**2 + (2.8282)**2)
r_yz = math.sqrt (2**2 + (2.8282)**2)
print " Projection of vector r in xz plane is ",round(r_xz,4),""
print " projection of vector r in yz plane is ",round(r_yz,4),""
import math
#Given that
v_w_x = 40 * math.cos(45 * pi / 180) # x component of wind blow in miles/h
v_w_y = 40 * math.sin(45 * pi /180) # y component of wind blow in miles/h
r_x = 200 # distance of destination point in x direction in miles
r_y = 0 # distance of destination point in y direction in miles
t = 40 # time taken by aeroplane to reach destination in minutes
print "Standard formula used is V = V1 + V2 + .....+ V_n "
v_x = (r_x)/t *60 # x - component of velocity required to reach destination in time in miles/h
v_y = r_y /t *60 # x - component of velocity required to reach destination in time in miles/h
v_p_x = v_x - v_w_x # x component of aeroplane velocity in miles/h
v_p_y = v_y - v_w_y # y component of aeroplane velocity in miles/h
print "Vector of velocity of pilot with respect to moving air is ",round(v_p_x,4)," +i ",round(v_p_y,4),"j miles/h where i and j stands for east and north respectively "
import math
#Given that
R_e = 6.4e6 # radius of earth in m
T = 8.64e4 # time period of one rotation of earth
theta1_pole = 90 # angle between pole and rotational axis
theta1_equator = 0 # angle between equator and rotational axis
g_pole = 9.8 # gravitational acceleration at pole in m/s**2
print "Standard formula used is g1 = g - R_e*f**2*(math.cos(theta1))**2 "
f = 2 * pi / T # rotational frequency of earth
g_equator = g_pole - R_e * f**2
del_g = g_pole - g_equator
print "Difference in gravitational acceleration at pole and equator is ",round(del_g,4)," m/s^2 "
import math
#Given that
R_e = 6.4e6 # radius of earth in m
theta1_pole = 90 # angle between pole and rotational axis
theta1_equator = 0 # angle between equator and rotational axis
g_pole = 10 # gravitational acceleration at pole in m/s**2
g_equator = 0 # gravitational acceleration at equator in m/s**2
print "Standard formula used is g1 = g - R_e*f**2*(math.cos(theta1))**2 "
f = math.sqrt (g_pole / R_e)
T = 2 * pi / f / 3.6e3
print "Angular velocity of Earth will be ",f," rad/s Time period would be ",round(T,4)," hours"
import math
#Given that
g_pole = 9.8 # gravitational acceleration at pole
m = 1 # mass of substance in kg
R_e = 6.4e6 # radius of earth in m
print "Standard formula used is coriolis force = -2*m*f x v "
g_equator = 0.75 *g_pole # gravitational acceleration at equator in m/s**2
f = math.sqrt ((g_pole - g_equator)/ R_e)
print "Angular velocity of Earth will be ",round(f,4)," rad/s . "
import math
#Given that
m = 1 # mass of particle in kg
theta1 = 30 # latitude position in degree
v = 0.5 # velocity of particle in km/s in north direction
print "Standard formula used is coriolis Force = 2*mass*angular velocity X velocity "
f_x = -2*m*2*pi * v*1000*(-1)*math.sin(theta1*pi/180)/86400 # coriolis force in east direction
f_z = -2*m*2*pi * v*1000*math.cos(theta1*pi/180)/86400 # coriolis force in verticle direction
F = math.sqrt(f_x**2+f_z**2)
alpha1 = -(math.atan(f_z/f_x)) *180 /pi
print "Magnitude and direction of coriolis force on particle are ",round(F,4)," N and ",round(alpha1,4)," degree with east respectively"