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Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was?
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Q.A running man has half the kinetic energy of a body of half his mass...
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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.
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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Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was?
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Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was?.
Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.A running man has half the kinetic energy of a body of half his mass. The man speeds up by 1.0ms^-1and then has the same kinetic energy as the boy . The original speed of the boy was?.
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