18. distances in space are often quoted in units of light years, the distance light travels in one year. (a) how many meters is a light year? (b) how many meters is it to andromeda, the nearest large galaxy, given that it is 2.00×106 light years away? (c) the most distant galaxy yet discovered is 12.0×109 light years away. how far is this in meters?

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?

Aspring has a relaxed length of 33 cm (0.33 m) and its spring stiffness is 6 n/m. you glue a 76 gram block (0.076 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 15 cm. you make sure the block is at rest, then at time t=0 you quickly move your hand away. the block begins to move upward, because the upward force on the block by the spring is greater than the downward force on the block by the earth. calculate y vs. time for the block during a 0.09-second interval after you release the block, by applying the momentum principle in three steps each of 0.03-second duration.

Which of these best describes the term ecliptic? a. the circle where "earth meets the sky" b. the change in azimuth and altitude of an object c. the point directly above the geographic north pole d. the path of the sun through the constellations of the zodiac