1) In any collision the momentum is conserved
(2*m)*(vo) + (m)*(-2*vo) = (2*m)(v1') + (m)(v2')
candel all the m factors (because they appear in all the terms on both sides of the equation)
2(vo) - 2(vo) = 2(v1') + (v2') => 2(v1') + v(2') = 0 => (v2') = - 2(v1')
2) Elastic collision => conservation of energy
=> [1/2] (2*m) (vo)^2 + [1/2](m)*(2*vo)^2 = [1/2](2*m)(v1')^2 + [1/2](m)(v2')^2
cancel all the 1/2 and m factors =>
2(vo)^2 + 4(vo)^2 = 2(v1')^2 + (v2')^2 =>
4(vo)^2 = 2(v1')^2 + (v2')^2
now replace (v2') = -2(v1')
=> 4(vo)^2 = 2(v1')^2 + [-2(v1')]^2 = 2(v1')^2 + 4(v1')^2 = 6(v1')^2 =>
(v1')^2 = [4/6] (vo)^2 =>
(v1')^2 = [2/3] (vo)^2 =>
(v1') = [√(2/3)]*(vo)
Answer: (v1') = [√(2/3)]*(vo)
The final velocity will be 19 m/sec.Option C is correct.
<h3>What is velocity?</h3>
The change of displacement with respect to time is defined as the velocity.
Velocity is a vector quantity. it is a time-based component. Velocity at any angle is resolved to get its component of x and y-direction.
From Newton's first equation of motion;

The final velocity will be 19 m/sec
Hence, option C is correct.
To learn more about the velocity refer to the link ;
brainly.com/question/862972
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Answer:
Acceleration is defined as the ratio between the change in velocity of an object and the time it takes for the object to change the velocity.
In formula, this is written as:

where
vf is the final velocity
vi is the initial velocity
t is the time it takes for the object to accelerate from u to v
Note that acceleration is a vector, so it can also be caused by a change in the direction of the velocity, not only by a change in its magnitude.
Answer:
multiply that and divided by 45