Question

The speed of the center of the earth as it orbits the sun is 107257 kmph and the absolute angular velocity of the earth about its north-south spin axis is 7.292(10-5) rad/s.Use the value for the radius of the earth as 6371 km and determine the velocities of points A, B, C, and D, all of which are on the equator. The inclination of the axis of the earth is neglected.

Answer 1

Answer with Explanation:

We are given that

Speed ,
`v_0`=107257 kmph

Angular velocity,
`\omega=7.292* 10^(-5) rad/s`

Radius of earth,r=
`6371 km=6371000 m`

1 km=1000 m

Linear velocity,
`v=r\omega=6371000* 7.292* 10^(-5)=464.57 m/s`

Linear velocity,
`v=464.57* (18)/(5)=1672.46 km/h`

Velocity at point A,
`v_A=-vi+v_0 j=-1672.46 i+107257j kmph`

Velocity at point B,
`v_B=v_0j-vj=107257j-1672.46j=105584.54j kmph`

Velocity at point C,
`v_C=v_0j+vi=1672.46 i+107257j kmph`

Velocity at point D,
`v_D=v_0j+vj=107257j+1672.46j=108929.46jkmph`