A ladder of length 17 ~m rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of 1 ~m / sec ., then when it is 8 ~m away from the wall, its upper end is coming down at the rate of

Step-by-step solution

In ABC , AC represents ladder AB vertical wall Let AB =x, BC =y ABC =90^ By Pythagoras theorem, aligned & AB ^2+ BC ^2= AC ^2 & x^2+y^2=17^2 & x^2=289-y^2 ... (i) & x^2=289-64 & x^2=225 & x=15 ~m aligned Consider equation (i), x^2=289-y^2 Differentiating w.r.t. t, we get aligned & 2 x d x dt =-2 y d y dt & 15 d x dt =-8(1) & d x dt = -8 15 ~m / s aligned Negative sign shows that the ladder is moving down. i.e., vertical length is decreasing Upper end is coming down at the rate of 8 15 ~m / s .