A child wanders slowly down a circular staircase from the top of a tower. With $x,y,z$ in feet and the origin at the base of the tower, her position $t$ minutes from the start is given by $$x=15\cos t,\quad y = 15 \sin t, \quad z = 100 - 5 t.$$

(a) How tall is the tower?
height = ft

(b) When does the child reach the bottom?
time = minutes

(c) What is her speed at time $t$?
speed = ft/min

(d) What is her acceleration at time $t$?
acceleration = ft/min${}^2$