Question

Answer and step please

1) two balls moving in opposite directions have velocities v1i,x=13m/s and v2i,x= -9m/s. If their masses are m1= 3.6_kg and m2=8.8_kg, respectively, and if their collision is perfectly elastic,then predict the velocity of each ball following the collision.

2) v2f,x=

Answer 1

In perfectly elastic collision, total kinetic energy and momentum is conserved.

so, momentum before collision = m1v1+m2v2=3.6*13-8.8*9= -32.4 kg m/s

Kinetic energy before collision =(m1v1^2+m2v2^2)/2= (3.6*13*13+8.8*9*9)/2=660.6 J

after collision let us take velocity of 3.6kg is v and 8.8kg is u.

so, apply momentum conservation 3.6v+8.8u=-32.4 .....(i)

v= (-32.4-8.8u)/3.6

apply conservation of energy= (3.6v^2+8.8u^2)/2= 660.6

=> 3.6v^2+8.8u^2= 660.6*2=1321.2 ......(ii)

solving equation (i) and (ii), for v and u

3.6*[(-32.4-8.8u)/3.6]^2+8.8u^2= 660.6*2=1321.2

=> u=3.77m/s

putting value of u in equation (i) v=-18.2 m/s