Saturday

January 31, 2015

January 31, 2015

Posted by **Preston** on Monday, November 1, 2010 at 5:17pm.

- Calc. -
**Reiny**, Monday, November 1, 2010 at 6:39pmThis is the classic problem that almost every text in Calculus uses to introduce "rate of change"

Make a diagram

Let the ladder by y ft above the ground, and

x ft away from the wall

so you have a right angled triangle

x^2 + y^2 = 25

2x dx/dt + 2y dy/dt = 0 (#1)

given : dx/dt = 2 ft/s

find : dy/dt when x = 7

when x = 7

49 + y^2 = 625

y = √576 = 24

back in #1

2(7)(2) + 2(24)dy/dt = 0

dy/dt = -28/48 = -7/12 ft/s

the negative indicates that the value of y is decreasing, or in other words, the ladder is dropping along the wall

**Answer this Question**

**Related Questions**

Calculus - A ladder is leaning against the wall of a house.The base of the ...

calculus - 1) A ladder 25 feet long is leaning against the wall of a house. The ...

Calculus--Please Help! - A 13-foot ladder is leaning against a vertical wall. If...

College Calculus - A 13-foot ladder is leaning against a vertical wall. If the ...

AICE math - A 30 foot ladder is leaning against a house(see figure). if the base...

Calculus - related rates: a ladder, 12 feet long, is leaning against a wall. if ...

Maths - a ladder 25ft long leans against a wall with its foot on level ground ...

Calculus - A 17 foot ladder is leaning against a wall. The bottom of the ladder...

Calculus - The top of a 24 foot ladder, leaning against a vertical wall, is ...

Calculus - A ladder 8 meters long is leaning against a wall. If the top of the ...