Answered

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A 20ft long ladder is leaning against a wall. The bottom of the ladder is sliding away from the wall at a rate of 2.5ft/sec. How fast is the top of the ladder sliding down when x=12ft ?

Sagot :

Chanlleidn

Answer:

-16/6 ft per sec (if my calculation isn’t wrong!).

Locate origin at the intersection of wall and floor. Measure positions of Top-end (say ‘y’) and Lower-end (say ‘x’) from the origin.x2+y2=length2" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">x2+y2=length2x2+y2=length2Since length is constant, differentiating above equation with respect to time we get :