Please help
The year is 2115. There is a high jump competition on planet Mars. An athlete of mass 72 kg who has been clearing a height of 2.44 m on Earth just the week before is competing here. What is the height this athlete can expect to clear in this competition?
Relevant data:
Mass of Mars = 6.421023 kg
Mass of Earth = 6.001024 kg
Radius of Mars = 3.40103 km
Radius of Earth = 6.38103 km
To determine the height the athlete can expect to clear in the high jump competition on Mars, we need to consider the effect of gravity on Mars compared to Earth.
The force of gravity experienced by an object is determined by the mass of the planet and the distance between the object and the center of the planet.
First, let's calculate the acceleration due to gravity on Mars using the mass and radius of Mars. The formula to calculate the acceleration due to gravity is:
g = (G * M) / r^2
where:
g is the acceleration due to gravity,
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the planet,
and r is the radius of the planet.
Substituting the known values for Mars:
g_mars = (G * M_mars) / r_mars^2
Next, let's determine the acceleration due to gravity on Earth using the same formula:
g_earth = (G * M_earth) / r_earth^2
Now, we can calculate the ratio of the acceleration due to gravity on Mars relative to Earth:
ratio = g_mars / g_earth
Finally, we can use the ratio to calculate the height the athlete can expect to clear on Mars compared to Earth.
height_mars = height_earth * ratio
Substituting the given values:
mass_earth = 6.001024 × 10^24 kg
mass_mars = 6.421023 × 10^23 kg
radius_earth = 6.38103 × 10^6 m
radius_mars = 3.40103 × 10^6 m
height_earth = 2.44 m
Now, let's plug these numbers into the formulas and calculate the result.