Question

Two smooth spheres \(\large A \) and \(\large B \) collide. The mass of \(\large A \) is four times that of \(\large B. \) The final velocities of \(\large A \) and \(\large B \) after collision are \(\large i +2j \) and \(\large -4i+7j \) respectively. If the initial velocity of \(\large A \) is \(\large -2i+5j \) and the linear momentum is conserved, find the initial velocity of \(\large B. \)

Answer 1

this belongs in physics, though im sure that if you post all formulas we'll figure this out.. i think it was something like, u calculate momentum which was something like mass times something else, and then u calculate final momentum, equate the equations, because momentum is conserved, and you're done

Answer 2

Sorry i haven't looked at physics in two years.

Answer 3

well momentum conserved after collision is \(\large M_{1}U_{1}+M_{2}U_{2}=M_{1}V_{1}+M_{2}V_{2} \) where M=mass , U=initial velocity and V=final velocity

Answer 4

oh okay this is simple then

Answer 5

Ma = 4Mb
V_fa = i+2j
V_fb = -4i+7j
V_ia = -2i+5j
V_ib - ?

Answer 6

Now set up the equation:
Ma*V_ia + Mb*V_ib = Ma*V_fa + Mb*V_fb

Answer 7

4Mb*(-2i+5j)+Mb*V_ib = 4Mb*(i+2j)+Mb*(-4i+7j)

Answer 8

While i compute this further, double check that i made all correct substitutions.

Answer 9

Mb*V_ib = 4Mb*(i+2j)+Mb*(-4i+7j) - 4Mb*(-2i+5j)
Divide everything by Mb
V_ib = 4*(i+2j)+(-4i+7j)-4*(-2i+5j)
V_ib = 4i + 8j - 4i + 7j +8i - 20j
V_ib = 8j + 7j + 8i - 20j
V_ib = 15j - 20j + 8i
V_ib = 8i - 5j

Answer 10

thanks :) i had to go on an errand :P just got back ;)