A15-meter ladder is leaning against a wall. the distance y(t) between the top of the ladder and the ground is decreasing at a rate of 6 meters per minute. at a certain instant t_0 start subscript, 0, end subscript, the bottom of the ladder is a distance x(t_0) start subscript, 0, end subscript, of 12 meters from the wall. what is the rate of change of the angle \theta(t) between the ground and the ladder at that instant?

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?