A 10.0g object moving to the right at 20.0 cm/s makes an elastic head on collision with a 15.0g object moving?

in the opposite direction at 30.0 cm/s. Find the velocity of each object after the collision.A 10.0g object moving to the right at 20.0 cm/s makes an elastic head on collision with a 15.0g object moving?
Prior to the collision, the 10.0g object has velocity 20.0 and the 15.0g object has velocity -30.0 . After the collision, the 10.0g object has velocity v1 and the 15.0g object has velocity v2.





Momentum is preserved, so


10(20)+15(-30)=10v1+15v2


-250=10v1+15v2


10v1=-250-15v2


v1=-25-1.5v2


Since the collision is elastic, kinetic energy is preserved, so


5(20)虏+7.5(-30)虏=5(v1)虏+7.5(v2)虏


8750=5(v1)虏+7.5(v2)虏


substituting for v1 we get


8750=5(-25-1.5v2)虏+7.5(v2)虏


8750=5(625+75v2+2.25v2虏)+7.5v2虏


8750=3125+375v2+11.25v2虏+7.5v2虏


0=-5625+375v2+18.75v2虏


using the quadratic formula, we get


v2= (-375 卤 750) / 37.5


which has two solutions: v2=-30 or v2=10


plugging these back into v1=-25-1.5v2 we get


v1=20 or v1=-40 respectively.





Solution #1: v1=20 %26amp; v2=-30 : This solution is impossible because it has the left-hand object moving to the right and the right-hand object moving to the left, as if they had passed right through each other.





Solution #2: v1=-40 and v2=10 : This is the correct solution. After the collision, the 10g object is moving 40.0 cm/s to the left and the 15g object is moving 10.0 cm/s to the right.