A block moves at 5 m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder h
ad been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks move along the x axis and the incident block?
1 answer:
Answer:
Speeds of 1.83 m/s and 6.83 m/s
Explanation:
Based on the law of conservation of momentum,
where m represents mass,
is the initial speed before impact,
and
are the velocities of the impacted object after the collision and of the originally stationary object after the impact.
Thus,
After the collision, the kinetic energy doubles, therefore:
Substituting the initial velocity of 5 m/s provides the equation needed to proceed.
We know that
leads to
Using the quadratic formula leads us to solve for the speeds after the explosion, specifically where a=2, b=-10, and c=-25.
By substituting the values, the solution yields results for the speeds of the blocks, which are ultimately 1.83 m/s and 6.83 m/s.
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