A cue ball of inertia m is given a speed v before it collides elastically with a full rack of 15 stationary balls in a game of pool. Each of the 16 balls has an inertia m.

1) What is the average speed of each ball after they fly apart. Express your answer in terms of some or all of the variables m and v.

2) What is the average momentum of each ball after they fly apart? Express your answer in terms of some or all of the variables m and v.

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?