A Diver Weighing 70 Kg Dives From A 10 M Platform. What Is Her Kinetic Energy Just Before Hitting The Water?A. 6860 J B. 4000 J C. 6000 J D. 5000 J

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Introduction

Kinetic energy is a fundamental concept in physics that describes the energy of motion. When an object moves, it possesses kinetic energy, which is directly proportional to its mass and the square of its velocity. In this article, we will explore the concept of kinetic energy and apply it to a real-world scenario: a diver weighing 70 kg diving from a 10 m platform.

Kinetic Energy Formula

The kinetic energy of an object can be calculated using the following formula:

KE = ½ mv²

Where:

  • KE is the kinetic energy of the object
  • m is the mass of the object
  • v is the velocity of the object

Calculating Kinetic Energy

To calculate the kinetic energy of the diver, we need to know her mass and velocity. We are given that the diver weighs 70 kg, but we need to calculate her velocity before hitting the water.

Assumptions

We assume that the diver falls from rest and accelerates downward due to gravity. We also assume that air resistance is negligible.

Calculating Velocity

Using the equation of motion:

s = ut + ½at²

Where:

  • s is the displacement (10 m)
  • u is the initial velocity (0 m/s)
  • t is the time of fall
  • a is the acceleration due to gravity (9.8 m/s²)

We can rearrange the equation to solve for time:

t = √(2s/a)

Substituting the values, we get:

t = √(2 × 10/9.8) = 1.02 s

Now, we can calculate the velocity using the equation:

v = u + at

Substituting the values, we get:

v = 0 + 9.8 × 1.02 = 10.016 m/s

Calculating Kinetic Energy

Now that we have the velocity, we can calculate the kinetic energy using the formula:

KE = ½ mv²

Substituting the values, we get:

KE = ½ × 70 × (10.016)² = 6860 J

Conclusion

In this article, we calculated the kinetic energy of a diver weighing 70 kg diving from a 10 m platform. We assumed that the diver falls from rest and accelerates downward due to gravity, and we calculated her velocity using the equation of motion. We then used the kinetic energy formula to calculate the kinetic energy of the diver, which was found to be 6860 J.

Answer

The correct answer is:

A. 6860 J

Discussion

This problem is a classic example of applying the concept of kinetic energy to a real-world scenario. The calculation involves using the equation of motion to calculate the velocity of the diver and then using the kinetic energy formula to calculate the kinetic energy.

Related Topics

  • Kinetic energy formula
  • Equation of motion
  • Acceleration due to gravity
  • Velocity calculation

Further Reading

Introduction

In our previous article, we calculated the kinetic energy of a diver weighing 70 kg diving from a 10 m platform. We assumed that the diver falls from rest and accelerates downward due to gravity, and we calculated her velocity using the equation of motion. We then used the kinetic energy formula to calculate the kinetic energy of the diver, which was found to be 6860 J.

Q&A

Q: What is the formula for kinetic energy?

A: The formula for kinetic energy is:

KE = ½ mv²

Where:

  • KE is the kinetic energy of the object
  • m is the mass of the object
  • v is the velocity of the object

Q: What is the mass of the diver in this problem?

A: The mass of the diver is 70 kg.

Q: What is the height of the platform from which the diver jumps?

A: The height of the platform is 10 m.

Q: What is the acceleration due to gravity?

A: The acceleration due to gravity is 9.8 m/s².

Q: How do we calculate the velocity of the diver?

A: We calculate the velocity of the diver using the equation of motion:

s = ut + ½at²

Where:

  • s is the displacement (10 m)
  • u is the initial velocity (0 m/s)
  • t is the time of fall
  • a is the acceleration due to gravity (9.8 m/s²)

Q: What is the time of fall for the diver?

A: We can calculate the time of fall using the equation:

t = √(2s/a)

Substituting the values, we get:

t = √(2 × 10/9.8) = 1.02 s

Q: What is the velocity of the diver just before hitting the water?

A: We can calculate the velocity of the diver using the equation:

v = u + at

Substituting the values, we get:

v = 0 + 9.8 × 1.02 = 10.016 m/s

Q: What is the kinetic energy of the diver just before hitting the water?

A: We can calculate the kinetic energy of the diver using the formula:

KE = ½ mv²

Substituting the values, we get:

KE = ½ × 70 × (10.016)² = 6860 J

Conclusion

In this Q&A article, we have answered some of the most frequently asked questions about the kinetic energy of a diver. We have covered topics such as the formula for kinetic energy, the mass and height of the diver, the acceleration due to gravity, and the calculation of velocity and kinetic energy.

Related Topics

  • Kinetic energy formula
  • Equation of motion
  • Acceleration due to gravity
  • Velocity calculation

Further Reading

Glossary

  • Kinetic energy: The energy of motion.
  • Mass: A measure of the amount of matter in an object.
  • Velocity: The rate of change of an object's position with respect to time.
  • Acceleration: The rate of change of an object's velocity with respect to time.
  • Displacement: The distance between an object's initial and final positions.