Question

From the top of a tower of vertical height ‘h’, a ball A is projected vertically upwards with speed v₀ at an angle of 60° with the horizontal. n second later a second ball B is projected horizontally with same speed v₀ . The two balls colloide with one another n is

(1) \(\frac{v_0}{g}\)

(2) \(\frac{2v_0}{\sqrt{3}g}\)

(3) \(\frac{2v_0}{g}\)

(4) \(\frac{v_0}{\sqrt{3}g}\)

Answer 1

 (2) \(\frac{2v_0}{\sqrt{3}g}\)

In Fig. O is top of tower. Choosing co-ordinate axis as shown in Fig. and t = 0 when ball A is projected; the instantaneous co-ordinates (x₁, y₁) of ball A are

The instantaneous co-ordinates (x₂ , y₂) at t = t (t > n) of ball B are

Let P be the point where the two balls colloide with one another. Co-ordinates of ball A and B are same at this moment of time. From Eqns. (1) and (3).

From Eqns (2) and (4); we have,

obviously, from Eqns. (5) and (6) we have