An arrow is shot using a bow. The arrow leaves the bow with a velocity of 45 m/s [forward] from a height of 10 meters. How long does it take the arrow to travel 135 m [forward]?

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

3. a lunar exploration vehicle was created by a research team. it weighs 3,000 kg on the earth. it needs an acceleration of 10 m/s2 on the moon. in order to have the same acceleration, what will be the net force acting on the vehicle on the earth?

Intro: a solid ball of radius rb has a uniform charge density ρ. part a: what is the magnitude of the electric field e(r) at a distance r> rb from the center of the ball? express your answer in terms of ρ, rb, r, and ϵ0. part b: what is the magnitude of the electric field e(r) at a distance r express your answer in terms of ρ, rb, r, and ϵ0. part c: let e(r) represent the electric field due to the charged ball throughout all of space. which of the following statements about the electric field are true? check all that apply. e(0) = 0 e(rb)=0 limr→∞e(r)=0 the maximum electric field occurs when r=0 the maximum electric field occurs when r=rb the maximum electric field occurs as r→∞.