Click the Game tab at the bottom of the simulation and select Level 1. (There is no seesaw balance for this part of the activity. ) Balance the first equation, and click Check to see if you got it right. If you can’t balance it in the first try, you can try again. Work through the five equations for Level 1. Click Continue to go on to Level 2, and later Level 3. Each level is more difficult than the one before. Keep trying until all the equations are balanced. In one or two sentences, describe how you did in the balancing game. In a few more sentences, explain one strategy you learned for balancing more complex equations.

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?