Answer to Question #109531 in Mechanics | Relativity for Clara

Question

Object A has an initial velocity of (10m/s, 0o). Object A has a mass of 5kg. Object B has a mass of 10kg and is initially at rest. After the collision, Object A heads off at an angle of 40o and Object B heads off at an angle of -20o. Calculate the velocity of each object after the collision.

Answer 1

In case of collision initial and final momentum is same

initial momentum =mv=5$\times$10$i$ + 0 = 50$i$

final momentum =(v_acos40 + v_bcos20)$i$ + (v_asin40 - v_bsin20)$j$

for initial to be equal to final the $j$ component must be zero

(v_asin40 - v_bsin20)=0

v_a(0.64)=v_b(0.34)

v_b=v_a(1.88) ..................(1)

now balancing the x component

v_acos40 + v_bcos20=50

v_a(0.76) + v_b(0.94) =50

substituting the value of v_b

v_a(0.76) + v_a(1.88)(0.94) = 50

2.5 v_a =50

v_a =20m/s

v_b =10.64 m/s