During an investigation, equal volumes of hot and cold baking soda solution and calcium chloride solution were mixed in four cups. A record of the investigation is shown below: Investigation Record
CupBaking Soda SolutionCalcium Chloride Solution
WHotCold
XColdCold
YColdHot
ZHotHot

Baking soda reacts with calcium chloride to form bubbles. In which cup will bubbles form the fastest?
Cup W
Cup X
Cup Y
Cup Z

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?