A stone is projected vertically upwards with velocity 40m/show that the stone will reach the point of projection with the same velocity
net displacement is zero, so there is no change in potential+kinetic energy.
PE = mgh, which has not changed, so KE also has not changed.
Hence, since mass has not changed, and mv^2 has not changed, neither has v^2.
However, v has changed from upward to downward. So, the question is poorly worded. The speed is the same, but the velocity has changed to the opposite direction.
To show that the stone will reach the point of projection with the same velocity, we can use the principle of conservation of mechanical energy.
Explanation:
1. Conservation of Mechanical Energy: According to the principle of conservation of mechanical energy, the total mechanical energy of a system remains constant as long as there are no external forces acting on the system.
2. At the highest point: When the stone reaches its maximum height, its velocity becomes zero. At this point, the entire initial kinetic energy is converted to potential energy.
3. At the point of projection: As the stone falls back down, its potential energy is converted back into kinetic energy. According to the principle of conservation of mechanical energy, the total mechanical energy must remain constant.
4. As a result, when the stone reaches the point of projection, it will have the same velocity as it had at the initial launch. This is because all the potential energy gained during the upward journey is converted back into kinetic energy.
Therefore, the stone will reach the point of projection with the same velocity of 40m/s.