Energy enables an object to do work. Work is done when A. no force is put on an object, and the object does not move in any direction. B. a force is put on an object, but the object does not move in any direction. C. a force is put on an object, and the object moves in the direction of the force. D. no force is put on an object, but the object moves at varying speeds in a random direction.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

The illuminance of a surface varies inversely with the square of its distance from the light source. if the illuminance of a surface is 120 lumens per square meter when its distance from a certain light source is 6 meters, by how many meters should the distance of the surface from the source be increased to reduce its illuminance to 30 lumens per square meter?

Which scientist was the first to propose the heliocentric model of the universe? a. aristotle b. isaac newton c. galileo galilei d. nicolaus copernicus