A particle is launched from the origin in R^3 with initial velocity v(0) = < 0, 8, 10 > and undergoes constant acceleration a = < 2, - 1, - 5 > due to the combined forces of gravity and wind.

The gravitational field of a spherical object  at any distance from it points back to the center of the object.  That is, in the field simulator it has arrows toward the center of the sphere.  Put a test mass in this field and  it will fall toward the center with increasing speed following the line of force.  Locally, the field is the acceleration of gravity at that point. Now,  how would you move a small mass so that you would not have to do work on it during the move? That work would be the change its energy.     You would move it radially toward the center.     You would move it radially away from the center.     You would move it perpendicularly to the line of force, that is, move it in a local plane that is perpendicular to the radius at that point.     There is no way to do this.  Any displacement direction will take work.

Current Attempt in Progress a In the figure, a horizontal force F of magnitude 18.0 N is applied to a 3.03 kg book as the book slides a distance d = 0.51 m up a frictionless ramp at angle 0 = 30°. (a) During the displacement, what is the net work done on the book by Fa, the gravitational force o the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed a the end of the displacement? Use g=9.81 m/s². ar (a) Number i (b) Number Units Units Psychology 8 +7

The force of attraction on an object below Earth’s surface is directly proportional to its distance from Earth’s center. Find the work done in moving a weight of w lb located a mi below Earth’s surface up to the surface itself. Assume Earth’s radius is a constant r mi.