A what mass of the small ball will cause the big ball to sto

Solution

Here bigger ball will first hit the ground and will bounce back with a velocity say V_bo with upward momentum. Just at this moment Smaller ball, with velocity V_so, will hit bigger ball with downward momentum.From conservation of linear momentum and bigger ball stops right after collision.

M_bV_bo-M_sV_so = M_sV_s

Since both balls have same speed before collsion say V_o,

So V_bo = V_so = V_o = SQRT[2gh] = SQRT [2x9.8x2.6] = 7.14 m/s

V_s = (M_b-M_s)V_o / M_s ........................................(1)

V_sis the speed of small ball after collision with bigger ball

Total KE before collsion = (1/2)(M_b+ M_s) V_o²

Total KE after collsion = (1/2)(M_s) V_s²

Since the collision is elastic, the kinetic energy before the collision is equal to the kinetic enery after collision.

So we get V_s² =(M_b + M_s) V_o² / M_s ...............................(2)

From equation 1 &2

M_s = M_b/3 = 1.32/3 = 0.44 kg

Vs = (M_b - M_b/3)V_o/(M_b/3) = 2V_o

So height reach by small ball H_max = V_s²/2g = 4V_o²/2g = 4(2gh)/2g = 4h = 4 x 2.6 = 10.4 meters