Question

し/ Problem 5 An object of mass m is tossed vertically upward, reaches a height h and returns to taking into account the Earth's the surface of the Earth. Neglecting friction, but rotation, der deflected from the vertical when it ive the expression for by how much, and in what direction, the object is strikes the surface. Use the method we followed lecture for a similar problem, where we ignored friction and second-order effects. Sire( y2 Eestn ard Show that a: 8 westward

Answer 1

The vector equation of motion for free fall under coriolis force is m r^rightarrow doubledot = -mg z^cap - 2 (w^rightarrow times r^rightarrow) m r^rightarrow doubledot = -g z^cap - 2 w^rightarrow times r^rightarrow dot because we have faster motion in the z - x plane, we can force in the z-direction, The considerable coriolis force is in the x - direction, comes from the z - component of velocity. And there is no coriolis force in the y-direction coming from z - component of velocity motion therefore x^doubledot = -2wz^dot sin theta 1 z^doubledot = -g integrate equation 2 z^dot = v_0 - g t z = v_0 t - 1/2 g t^2 where z^dot (0) = v_0 z(0) = 0 therefore x^doubledot = -2w (v_0 - gt) sin theta x^dot = -2 w sin theta (v_0 t - 1/2 g t^2) note that x^dot(0) = 0 is used as be \r\n integrating one more time x = -2 w sin theta integral (v_0 t - 1/2 g t^2) dt