A ladder 5m is resting against vertical waall.The bottom of the ladder is pulled along the ground away from the wall at the rate of 1.5m/sec.The length of the highest point of the ladder when the foot of the ladder is 4.0m away from the wall decreases at the rate of

hi, let the length of the highest point of the ladder = h distance of the bottom from wall = d so, h^2 + d^2 = 5^2 h^2 + d^2 = 25 h = (25 - d^2 )^1/2 dh/dt = - 1/2 (25 - d^2 )^ -1/2 * 2d = - 4 / 3 , rate of decreas of h 4/3 m/s

Hi, let a be vertical height & b be distance of bottom from wall, so a^2 + b^2 =25 when b = 4m then a = 3m & Diff. above w.r.t. dt, we can find speed of highest point