Problem:

A stone of mass 2kg is falling from rest from the top of a hill. What will be the kinetic energy after 15 seconds?

Solution:

To calculate the kinetic energy of the stone after 15 seconds, we need to consider the concept of gravitational potential energy and the principle of conservation of energy.

Step 1: Understand the Concept

In this problem, the stone is falling from rest, which means it initially has only potential energy due to its position at the top of the hill. As the stone falls, its potential energy is converted into kinetic energy. According to the principle of conservation of energy, the total mechanical energy (potential energy + kinetic energy) of the stone remains constant throughout its fall.

Step 2: Calculate Potential Energy

The potential energy of an object at a certain height is given by the equation:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Since the stone is falling from the top of the hill, we can assume the height is the maximum height of the hill. However, the given problem does not provide the height of the hill. Therefore, we cannot calculate the exact potential energy. However, we can proceed with the assumption that the stone is falling from a significant height, which means its potential energy is high.

Step 3: Calculate Kinetic Energy

The kinetic energy of an object is given by the equation:

Kinetic Energy (KE) = 0.5 * mass (m) * velocity^2

To calculate the kinetic energy of the stone after 15 seconds, we need to determine its velocity at that time. We can use the equation of motion:

Final Velocity (v) = Initial Velocity (u) + (acceleration (a) * time (t))

Since the stone is falling freely under the influence of gravity, its acceleration is equal to the gravitational acceleration (g = 9.8 m/s^2). The initial velocity (u) is 0 m/s since the stone is falling from rest.

Therefore, the final velocity (v) of the stone after 15 seconds can be calculated as:

v = 0 + (9.8 * 15)
v = 147 m/s

Now we can substitute the mass (m = 2 kg) and the final velocity (v = 147 m/s) into the kinetic energy equation:

KE = 0.5 * 2 * 147^2
KE = 0.5 * 2 * 21609
KE = 21609 J

Answer:

The kinetic energy of the stone after 15 seconds of falling will be 21609 Joules.

V = u + atv = 0 + 10 × 15v= 150 m/sk = 1/2 mv^2k = 1/2 × 2 ×150×150k = 22500 joules