Question

A 20 ft ladder leans against a wall. The bottom of the ladder is 5 ft from the wall at time t=0 and slides away from the wall at a rate of 2ft/sec.

Find the velocity of the top of the ladder at time t=2.

The velocity of ladder at time t=2 is

Answer 1

\[u^2+v^2=20^2\]

Answer 2

u(0)=5
u'=2

Answer 3

find v'(2)

Answer 4

\[u(1)=5+2, u(2)=7+2=9\]

Answer 5

\[2uu'+2vv'=0\]

Answer 6

\[v'=\frac{-u u'}{v}\]

Answer 7

\[v'(2)=\frac{-u(2)u'(2)}{v(2)}=\frac{-9(2)}{\sqrt{400-9^2}}\]