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A man who is running has half the kinetic energy of the boy of half his mass was. The man speed up by 1.0m/s and then has the same kinetic energy as the boy. What was the original speed of the man?
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A man who is running has half the kinetic energy of the boy of half hi...

Given Information:
- The man has half the kinetic energy of the boy of half his mass.
- The man speeds up by 1.0m/s and then has the same kinetic energy as the boy.

Let's solve the problem step by step:

Step 1: Understanding the Kinetic Energy formula
- Kinetic Energy (KE) = 0.5 * mass * velocity^2

Step 2: Establishing the initial situation
- Let the mass of the boy be 'm' and his initial speed be 'v'.
- Therefore, the initial kinetic energy of the boy = 0.5 * m * v^2

Step 3: Defining the initial situation of the man
- The mass of the man would be '2m' (half of the boy's mass).
- Given, the man has half the kinetic energy of the boy.
- Initial kinetic energy of the man = 0.5 * 2m * u^2, where 'u' is the initial speed of the man.

Step 4: Equating the initial kinetic energies
- 0.5 * 2m * u^2 = 0.5 * m * v^2
- 2u^2 = v^2
- u = v/√2

Step 5: Finding the final speeds
- The man speeds up by 1.0m/s, so his final speed is 'u+1'.
- The boy's final speed remains 'v'.
- Given, the final kinetic energies of both are equal.
- 0.5 * 2m * (u+1)^2 = 0.5 * m * v^2

Step 6: Solving for the initial speed of the man
- Substitute the value of 'u' from Step 4 into the equation obtained in Step 5 and solve for 'v'.
- Once 'v' is found, calculate the initial speed of the man by substituting back into 'u = v/√2'.

Therefore, the original speed of the man can be calculated using the above steps and equations.
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A man who is running has half the kinetic energy of the boy of half his mass was. The man speed up by 1.0m/s and then has the same kinetic energy as the boy. What was the original speed of the man?
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