Q.A running man has half the kinetic energy of a body of half his mass...
Q.A running man has half the kinetic energy of a body of half his mass...
Introduction:
In this problem, we are given that a running man has half the kinetic energy of a body of half his mass. We are also told that when the man speeds up by 1.0 m/s, he has the same kinetic energy as the boy. We need to find the original speed of the boy.
Given:
- The running man has half the kinetic energy of a body of half his mass.
- When the man speeds up by 1.0 m/s, he has the same kinetic energy as the boy.
Let's solve the problem step by step:
Step 1: Understanding Kinetic Energy
Kinetic energy is given by the equation: K.E. = 1/2 * m * v^2, where K.E. is the kinetic energy, m is the mass, and v is the velocity.
Step 2: Expressing the Given Information
- The running man has half the kinetic energy of a body of half his mass. This can be written as:
K.E.(man) = 1/2 * (1/2)m * v^2
- When the man speeds up by 1.0 m/s, he has the same kinetic energy as the boy. Let's assume the original velocity of the boy is v0. After speeding up, the velocity becomes v0 + 1.0 m/s. Thus, we can write:
K.E.(man) = K.E.(boy)
1/2 * (1/2)m * v^2 = 1/2 * m * (v0 + 1.0)^2
Step 3: Solving the Equation
Let's solve the equation for the original velocity of the boy (v0).
1/2 * (1/2)m * v^2 = 1/2 * m * (v0 + 1.0)^2
Simplifying the equation, we get:
1/2 * (1/2)v^2 = (v0 + 1.0)^2
Taking the square root on both sides, we have:
1/2 * (1/2)v = v0 + 1.0
1/4 * v = v0 + 1.0
v0 = 1/4 * v - 1.0
Step 4: Finding the Original Speed of the Boy
To find the original speed of the boy (v0), we need to substitute the given values into the equation. However, we don't have a specific value for the velocity (v) of the running man. Therefore, we cannot determine the exact original speed of the boy without additional information.
However, if we assume a value for the velocity of the running man, we can calculate the corresponding original speed of the boy using the equation v0 = 1/4 * v - 1.0.
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