A ball with a mass of 5 kg is rolling at 12 m/s and elastically collides with a resting ball with a mass of 9 kg. What are the post-collision velocities of the balls?

1 Answer
Apr 17, 2016

u_1=-24/7 m/s
u_2=60/7" "m/s
"TESTING"
color(green)(E_b=E_a)

Explanation:

enter image source here
"using the equation (1)"

5*12+9*0=5*u_1+9*u_2
60+0=5*u_1+9*u_2

60=5*u_1+9*u_2" (a)"

"using the equation (3)"

12+u_1=0+u_2

u_2=12+u_1 " (b)"

"now use (a)"

60=5*u_1+9*(12+u_1)

60=5*u_1+108+9*u_1

60-108=14*u_1

-48=14*u_1

u_1=-48/14=-24/7 m/s

"finally ;use (b)"

u_2=12-24/7

u_2=(84-24)/7

u_2=60/7" "m/s

"testing"

"The Total Kinetic Energy before collision:"
E_b=1/2*5*12^2+0

E_b=72*5=360J

"The Total Kinetic Energy after collision:"

E_a=1/2*5*(-24/7)^2+1/2*9*(60/7)^2

E_a=(5*576)/(2*49)+(9*3600)/(2*49)

E_a=(2880+32400)/98

E_a=35280/98

E_a=360J

color(green)(E_b=E_a)