Module 14  Answers 
Lesson 1 
Answer 1 
14.1.1 The bottom of the ladder moves at a constant rate of 3 ft/sec while the top of the ladder falls at an increasing rate. 
Answer 2 
14.1.2 . The negative sign indicates that y is decreasing. 
Answer 3 
14.1.3 The velocity of the ladder's top is given by 
Answer 4 
14.1.4
Solving yt2(t)=0 indicates that the top of the ladder hits the ground after 5 seconds, but
is undefined at that time. As t approaches 5 seconds,
grows without bound. So in theory the top is going infinitely fast when it hits the ground as suggested by the following figure.

Lesson 2 
Answer 1 
14.2.1
The parametric equations that model the ladder's position at time t are shown in the screen below.

Answer 2 
14.2.2 The top of the ladder is falling at an increasing rate while the bottom is moving at a decreasing rate. 
Answer 3 
14.2.3 Using the derivative of the position of the bottom of the ladder, xt2(t), and evaluating it at the given times, the bottom is moving at approximately 21.2015 ft/sec, 17.2582 ft/sec, and 8.5665 ft/sec, respectively. 
Lesson 3 
Answer 1 
14.3.1
About 61.0 nautical miles.

Answer 2 
14.3.2

Self Test 
Answer 1 
x(t) = 0 y(t) = 15 – 45t 
Answer 2 
x(t) = 24 – 52t y(t) = 0 
Answer 3 
The car coming from the North will arrive at the intersection first. 
Answer 4 
Define 
Answer 5 
with t = 0.25 is approximately 63.739, so the distance between the cars is decreasing at a rate of 63.739 mph. 
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