The gravitational force on a point mass m due to a point mass m at the origin is a gradient field with potential u(r)= (gmm)/r , where g is the gravitational constant and r = (x^2 + y^2 + x^2)^(1/2) is the distance between the masses a. find the components of the gravitational force in the x-, y-, and z-directions, where f(x, y,z) = -gradientu(x, y,z) b. show that the gravitational force points in the radial direction (outward from point mass m) and the radial component is f(r) = (gmm)/(r^2) c. show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of u

How many seconds does it take a pebble released from rest off a bridge to fall 29.4 m ? what is the pebble's speed when it has fallen 29.4 m ?

Researchers determine that the biodiversity in a woodland region is declining. they identify two major threats to the region's biodiversity, a method to address each threat, and the expected outcome of each method. this information is shown in the table. a) reforestation would not benefit many species because most forest species live on the ground. b) reforestation would take the longest time to be effective because trees take several years to grow. c) biological augmentation would benefit only a few species because is is typically not very effective. d) biological augmentation would take less time to ve effective because it targets the majority of prey species.

An electromagnet is a device in which moving electric chargers in a coil of wire create a magnet. whats one advantage of using electromagnetic in devices