Question

A 16 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground?

Answer 1

I Think i know how to do this but its not accepting my answer

Answer 2

I drew my triangle 16ft 13ft 9.327ft

Answer 3

then i took the a^2+b^2=c^2 and took the derivative

Answer 4

i plugged in my numbers for a b c then plugged in for 1 for the rate of c and -3 for the rate of b

Answer 5

y = 13 correct?

Answer 6

x should be 9.27

Answer 7

Before you put in 13, you have to leave it as the variable y.
Use x^2 + y^2 = 16^2

Differentiate throughout with respect to t.

Tell me what you get.

Answer 8

2x(dx/dt)+2y(dy/dt)=256

Answer 9

well actually = 0

Answer 10

right. Now put dy/dt = -3, y = 13. Find x using pythagoras theorem and put that value and solve for dx/dt.

Answer 11

2x(dx/dt)-78=256

Answer 12

so 2x(dx/dt)=334

Answer 13

there is no 256. The right side is 0 when you take the derivative.

Answer 14

shoot sorry i forgot 2x(dx/dt) = 78

Answer 15

2x(dx/dt) + 2y(dy/dt) = 0
Divide by 2 throughout
x(dx/dt) + y(dy/dt) = 0
dy/dt = -3, y = 13
x(dx/dt) = 39
dx/dt = 39/x.

From the right angle we know x = sqrt(16^2 - 13^2)
Solve for dx/dt

Answer 16

ahhhh i see my problem

Answer 17

i was taking the derivative first instead of = 0

Answer 18

i got 4.1812 for my final

Answer 19

cool. I don't know what decimal accuracy it needs. But 4.18 or 4.2 should be acceptable..

Answer 20

just tried it. it worked. Thanks for the help. When doing problems with the pathagoreon theorem like these do you always make your C 0?

Answer 21

Not sure what you mean by "make you C 0".

Answer 22

well i mean do you always plug in C before taking the derivative?

Answer 23

C is the ladder length and it is fixed at 16 feet. So no matter how low or high the ladder rests, the x^2 and y^2 will always add up to the square of the ladder length.
So x^2 + y^2 = 16^2.

Answer 24

ohhh ok i understand. so because the ladder is a constant

Answer 25

But when you take the derivative, the right hand side will be zero because it is a constant.

Answer 26

I understand. makes alot more sense now

Answer 27

cool.