At the instant the displacement of a 2.00 kg object relative to the origin is = (2.00 m) + (4.00 m) - (3.00 m) , its velocity is = - (5.85 m/s) + (2.10 m/s) + (8.31 m/s) and it is subject to a force = (9.47 N) - (6.28 N) + (6.46 N) . Find the acceleration of the object ((a), (b) and (c) for , and components respectively), the angular momentum of the object about the origin ((d), (e) and (f) for , and components respectively), the torque about the origin acting on the object ((g), (h) and (i) for , and components respectively), and (j) the angle between the velocity of the object and the force acting on the object.

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?