On Mars, the gravitational attraction is 1/4 compared to that on the Earth. When an object is thrown up on the Earth, the maximum height it reaches is 200 m. If the same object were thrown in the same way on Mars how many meters would it rise. Please provide potential and kinetic energy involved.
The gravitational potential energy of an object with mass m on any planet is given by the general formula PE = m*g*h where m is the mass of the object, g is the gravitational acceleration due to the force of attraction between the planet and the object, this is dependent on the mass of the planet and its radius and h is the distance between the object and the surface of the planet.
Here, it is given that the gravitational acceleration on Mars is one fourth that of the gravitational attraction on the Earth. When an object is thrown up here, it reaches a maximum height of 200 m. The gravitational potential energy of the object at a height of 200 m is m*g*200.
The same object is thrown up in a similar way on Mars. If the object rises to a maximum height of H, the gravitational potential energy at that height should equal m*g*200.
As the gravitational acceleration is one fourth on Mars, m*(g/4)*H = m*g*200
=> H = 200*4 = 800
On Mars, the object rises to a height of 800 m.