1. earth is located at one of the moon's orbit.2. according to kepler's second law, jupiter will be traveling most slowly around the sun when at .3. earth orbits in the shape of a/an around the sun.4. the mathematical form of kepler's third law measures the period in years and the in astronomical units (au).5. according to kepler's second law, pluto will be traveling fastest around the sun when at .6. the extent to which mars' orbit differs from a perfect circle is called its:

If vx = 7.00 units and vy = -7.60 units, determine the magnitude of v⃗ . determine the direction of v⃗ .

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?

Arope has one end tied to a vertical support. you hold the other end so that the rope is horizontal. if you move the end of the rope back and forth with a frequency of 4 hz, the transverse wave you produce has a wavelength of 0.5 m. what is the speed of the wave in the rope?