Question

A 4.00 kg object is moving at 5.00 m/s EAST. It strikes a 6.00 kg that is at rest. The objects have an elastic collision. The velocity of the 4.00 kg object after the collision is at an angle of 30.0 degrees SOUTH of EAST. The velocity of the 4.00 kg mass after the collision is

5.78 m/s
4.56 m/s
3.55 m/s
1.67 m/s

Answer 1

3.55 work done#########

Answer 2

Answer:

The velocity of the mass 4 kg after the collision will be 2m/s.

Explanation:

To solve this problem we will use the concept of conservation of momentum in elastic collision.

In elastic collision, the momentum is always conserved.

The required equations  to solve this problem is,

 $M$₁$u$₁$+M$₂$u$₂$=M$₁$V'$₁$+$$M$₂$V$₂(1)

           $e=V$₂$-V'$₁$/u$₁$-u$₂     (2)

$e$= coefficient of elasticity

$M$₁=4kg$u1$

$u$₁=5$m/s$

$M$₂=6kg

$u$₂=0

 $V'$₁=$V$₁$sin30$°(3)

(as per question 4 kg object after collision goes 30° south of east)

$e$=1 for elastic collision

sin30°=1$/$2

by putting this in equation (2) we get;

$1=V$₂$-V$₁$sin30$°$/5$

$5=V$₂$-V$₁$sin30$°

$V$₂$=5+V$₁$sin30$°            (4)

By putting equation (4) in equation (1) we get;

$4$×$5+6$×$0=4$×$V$₁$sin30$°$+6(5+V$₁$sin30$°$)$

$20=2V$₁$+30+3V$₁

$5V$₁$=-10$

$V$₁$=-2$$m/s$

Here the negative sign indicates the direction of velocity. Hence, the velocity of mass 4kg after the collision will be 2$m/s$.