A(n) 5 kg object moving with a speed of 8.7 m/s collides with a(n) 18 kg object moving with a velocity of 11 m/s in a direction 20◦ from the initial direction of motion of the 5 kg object. 8.7 m/s 11 m/s 18 kg 5 kg 20◦ What is the speed of the two objects after the collision if they remain stuck together? Answer in units of m/s.

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?