##### Question

# a 13-ft ladder is leaning against a wall

a 13-ft ladder is leaning against a wall. suppose that the base of the ladder sides away from the wall at the constant rate of 3ft/sec

1. explain why the motion of the two ends of the ladder can be represented by the parametric equations:

x1(t)=3t, y2(t)=0

x2(t)=0, y2(t)= radical(13^2-(3t)^2)

2. what values of t make sense in this problem situation?

3. use stimultaneous mode. give a viewing window that shows the action.(Hint: it may be helpful to "hide" th ecoordinate axes if your grapher has this feature. if not, adjust the parametric equation to move th eaction away from the axes)

4. use analytic method to find the rate at which the top of the ladder is moving down the wall at t=0.5, 1, 1.5, and 2sec. in theory, how fast is the top of the ladder moving as it hit the ground?