Question

AB is a rod of length 2m. It is placed against a vertical wall with its end A is in contact with wall. The end B of rod (in contact with horizontal floor) is pulled along the floor with a constant speed of 0.5 ms^-1. The speed of the end A of the rod when it makes angle of 37° with floor is

(1) 0.4 ms^-1

(2) 0.3 ms^-1

(3) 0.5 ms^-1

(4) 0.67 ms^-1

Answer 1

(2) 0.3 ms^-1

Fig shows ladder when θ = 37° .

Let (x, 0) and (0, y) be the instantaneous co-ordinates of end B and A respectively. The length AB = l of rod is  l² = x² + y²

Differentiate w.r.t time (t)

Therefore, velocity of end A; v_A is

Negative sign indicates that end A moves vertially downwards.