An object with a mass of 7 kg is thrown straight upward on Earth at a speed of 4

Question

An object with a mass of 7 kg is thrown straight upward on Earth at a speed of 49.41 m/s. Due to air resistance, i.e., non-conservative work, it only reaches a maximum displacement of 45.4 meters. If the object were thrown at the same speed straight upwards on another planet where the mass of the planet was a factor of 2 larger than that of earth and its radius was a factor of 3.8 smaller than earth, what would its maximum vertical displacement be, in meters, on this new planet if the amount of energy lost to non-conservative forces was a factor of 2.3 smaller than that of earth?

Explanation / Answer

Let the potential energy is zero on surface .

energy lost on Earth = initial KE - final PE = 0.5mv^2 - mgh = 0.5*7*49.41^2 - 7*9.8*45.4 = 5430 J

Energy lost on other planet = 5430/2.3 = 2361 J

gravity g on other planet = 9.8* 2*3.8^2 = 283 m/s^2

potential energy increase at maximum displacement = mgh = 0.5mv^2 - energy lost = 0.5*7*49.41^2 - 2361

= 6183.7 J

height h = 6183.7/(7*283) = 3.12 m answer

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