AP Calculus AB
Day 12
Section 2.6
3/23/2016
Perkins
1. The base of a 25-foot ladder is being pulled away from the house it
leans on at a rate of 4 feet per second. At what rate is the top of the
ladder moving when the base of the ladder is 7 feet from the building?
dy
Find
.
dt
dx
 4 ft sec
dt
x  7 feet
x 2  y 2  25
dx
dy
2 x  2y  0
dt
dt
25
dy
24
2  7  4   2y  0
dt
7
dy
2  7  4   2  24   0
dt
dy 56 7 ft


sec
dt 48
6
25
y
x
2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second
away from a light that is 13 feet above the ground. Find the rate at
which his shadow’s length is changing when he is 10 feet from the base
of the light.
13 d

6 s
13s  6d
13s  6x  6s
7s  6x
ds
dx
7 6
dt
dt
ds
7  6 4
dt
ds 24 ft

sec
dt 7
ds
Find
.
dt
13 ft
6
x
s
d
d  x s
dx
 4 ft sec
dt
x  10 ft
2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second
away from a light that is 13 feet above the ground. Find the rate at
which the position of the tip of his shadow is changing when he is 10
feet from the base of the light.
dd
Find
.
dt
dx
 4 ft sec
dt
x  10 ft
13 ft
6
x
s
d
ds 24 ft

sec
dt 7
d  x s
dd dx ds
24 52 ft


 4

sec
dt dt dt
7
7
3. A fishing line is reeled in at a rate of 1 foot per second from a bridge
that is 15 feet above the water. At what rate is the angle between the
line and the water changing when 25 feet of line is out?
d
Find
.
dt
dr
 1ft sec
dt
r  25 feet
15
1

15r
sin 
r
d
2 dr
cos
 15r
dt
dt
15
 20  d
 25  dt
 

 25
1
2
d
15  25 
3 rad


sec

2
dt  25   20  100
r
15

x
25

20
15
AP Calculus AB
Day 12
Section 2.6
Perkins
1. The base of a 25-foot ladder is being pulled away from the house it
leans on at a rate of 4 feet per second. At what rate is the top of the
ladder moving when the base of the ladder is 7 feet from the building?
2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second
away from a light that is 13 feet above the ground. Find the rate at
which his shadow’s length is changing when he is 10 feet from the base
of the light.
2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second
away from a light that is 13 feet above the ground. Find the rate at
which the position of the tip of his shadow is changing when he is 10
feet from the base of the light.
3. A fishing line is reeled in at a rate of 1 foot per second from a bridge
that is 15 feet above the water. At what rate is the angle between the
line and the water changing when 25 feet of line is out?