Question

a ladder which is 15ft leans against a wall. suppose that when the bottom of the ladder is x feet away from the wall,the bottom is being pushed towards the wall at a rate of 1/2x feet per second. how fast is the top of the ladder rising at the moment the bottom is 5 feet from the wall?


so i did pythagerous and i figured out the other side which was 14.14, since that is the y side or the height of the wall at a point where the ladder is 5 feet from the wall

from there i ddid the derivative of
x^2 + y^ 2 = c^2
which was
2x(dx/dt) + 2y(dy/dt) = 0 ( this is 0 cuz the hypothenouse is constant)

and then i subbed in the numbers and solved for dy/dt
the numbers i subbed in were
a = 5
y = 14.14
dx/dt= 0.5

and im getting -.0.176 as my answer but the correct answer for some reason is 0.884 , can someoen tell me what im doing wrong?

thanks a lot

Answer 1

x/dt = - 1/2 it is getting smaller.
5 (-.5) + 14.14 (dy/dt) = 0
dy/dt = .176
so I agree with you except for the sign.

Answer 2

okay so other than the sign are you saying what im doing is correct? and the answer is most likely wrong?

Answer 3

Yes.