# A Man and a Grasshopper Jumping Upward: A Height Comparison

If a man and a grasshopper both jump upward with the same initial velocity and the grasshopper achieves a height of 5 cm, what will be the height achieved by the man?

## The Height Achieved by the Man

When the man and the grasshopper both jump upward with the same initial velocity, they experience the same gravitational force acting on them. This force causes them to decelerate as they move upward. Since both the man and the grasshopper have the same initial velocity, their initial kinetic energies are the same. As they move upward, this kinetic energy gets converted into potential energy due to their increase in height.

**Potential energy of an object** is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height. Since the mass and acceleration due to gravity are the same for both the man and the grasshopper, their potential energies will be directly proportional to their heights.

As the grasshopper achieved a height of 5 cm, the man will achieve a greater height than 5 cm due to their potential energies being directly proportional to their heights. The exact height achieved by the man will depend on factors such as the mass of the man and the accuracy of the initial velocity. However, it can be confidently stated that the height achieved by the man will be greater than 5 cm.