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A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2?
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A man throws a ball vertically up in the air with an initial velocity ...
- **Understanding the Problem**
The problem involves a man throwing a ball vertically up with two different initial velocities, v1 and v2, such that the ball reaches a maximum height of 12 m in both cases. We need to calculate the ratio v1/v2.
- **Using the Principle of Conservation of Energy**
When the ball reaches its maximum height, all of its initial kinetic energy is converted into potential energy. We can set up the equation as:
Initial kinetic energy = Final potential energy
- **Calculating the Initial Kinetic Energy**
The initial kinetic energy of the ball is given by:
KE = 0.5 * m * v^2
where m is the mass of the ball and v is the initial velocity.
- **Calculating the Final Potential Energy**
At the maximum height, the potential energy of the ball is given by:
PE = m * g * h
where g is the acceleration due to gravity and h is the maximum height.
- **Setting up the Equation**
Since the ball reaches the same height in both cases, we can set up the following equation:
0.5 * m * v1^2 = m * g * 12
0.5 * m * v2^2 = m * g * 12
- **Solving for v1/v2**
By dividing the two equations, we get:
(v1/v2)^2 = 1
v1/v2 = 1
Therefore, the ratio v1/v2 is 1. This means that the initial velocities v1 and v2 are equal.
The problem involves a man throwing a ball vertically up with two different initial velocities, v1 and v2, such that the ball reaches a maximum height of 12 m in both cases. We need to calculate the ratio v1/v2.
- **Using the Principle of Conservation of Energy**
When the ball reaches its maximum height, all of its initial kinetic energy is converted into potential energy. We can set up the equation as:
Initial kinetic energy = Final potential energy
- **Calculating the Initial Kinetic Energy**
The initial kinetic energy of the ball is given by:
KE = 0.5 * m * v^2
where m is the mass of the ball and v is the initial velocity.
- **Calculating the Final Potential Energy**
At the maximum height, the potential energy of the ball is given by:
PE = m * g * h
where g is the acceleration due to gravity and h is the maximum height.
- **Setting up the Equation**
Since the ball reaches the same height in both cases, we can set up the following equation:
0.5 * m * v1^2 = m * g * 12
0.5 * m * v2^2 = m * g * 12
- **Solving for v1/v2**
By dividing the two equations, we get:
(v1/v2)^2 = 1
v1/v2 = 1
Therefore, the ratio v1/v2 is 1. This means that the initial velocities v1 and v2 are equal.
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A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2?
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A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2?.
A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v2 such that it reaches a maximum height of 12 m. Calculate v1/v2?.
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