Agolf ball is hit off a tee at the edge of a cliff. its x and y coordinates as functions of time are given by x 5 18.0t and y 5 4.00t 2 4.90t2, where x and y are in meters and t is in seconds. (a) write a vector expression for the ball's position as a function of time, using the unit vectors i^ and j^. by taking derivatives, obtain expressions for (b) the velocity vector vs as a function of time and (c) the acceleration vector as as a function of time. (d) next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t 5 3.00 s.

The gravitational attraction between two objects will if one object acquires more mass .

Because air contracts as it cools, the air pressure inside a freezer is typically lower than on the outside. why do ice cubes inside a freezer tend to shrink over time? a. the ice dissolves oxygen from the air, forming a denser crystalline matrix.b. the ice reacts chemically with carbon dioxide in the air, forming gaseous carbon compounds.c. the ice melts, and then the liquid freezes as ice crystals on the bottom of the freezer.d. the ice sublimes, and then the water vapor deposits as ice crystals on the sides of the freezer.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants