A child wanders slowly down a circular staircase from the top of a tower. Withx,y,z

x,y,zin feet and the origin at the base of the tower, her positiont

tminutes from the start is given by

x=30cost,y=30sint,z=1205t.

A) Determine her speed and acceleration at time t

2) A particle starts at the pointP=(5,4,2) and moves along a straight line towardQ=(2,2,5)at a speed of 2 cm/sec. Letx,y, zbe measured in centimeters andt be measured in seconds

(a)Find the particle's velocity vector. v(t)

b) Find parametric equations for the particle's motion. x(t) y(t) z(t)

3) Supposer(t)=cos(t)i+sin(t)j+3tk represents the position of a particle on a helix, wherez is the height of the particle.

When the particle has height9 it leaves the helix and moves along the tangent line at the constant velocity

Find a vector parametric equation for the position of the particle (in terms of the original parametert as it moves along this tangent line

4) A stone is thrown from a rooftop at timet=0

t=0seconds. Its position at timet is given byr(t)=4ti2tj+(9.84.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vectori points east,j points north, andk points up.

How fast is the stone moving when it hits the ground?