Answer:
91.5 km
Explanation:
Hi!
If we are to ignore the variation in gravity we can use the formula for teh potential energy near the surface of a planet:
mgh
If the energy of the material ejected from the volcano on Io's surface is the same on earth's surface we have:
where subindexes Io and e means Jupiter's moon Io, and Earth, respectively
solving for h_e
The acceleration due to the gravity of a planet can be calculated as:
Where R and m are the radius and mass of the planet
Therefore:
m_e = 5,972 × 10^24 kg
R_e = 6 371 km
Replacing all given values:
h_e = 500 km *(0.183) = 91.515 990 km
The value of the final speed depends on the mass of the ore.
Let's call m the mass of the ore. We can solve the exercise by requiring the conservation of momentum, which must be the same before and after the ore is loaded.
Initially, there is only the cart, so the momentum is
After the ore is loaded, the new mass will be (1200 kg+m), and the new speed is
. The momentum p is conserved, so it is still 12960 kg m/s. Therefore, we have
and so the final speed is
<span>We know that the momentum keeps constant in a inelastic collisions, so the product of mass and speed do not change:
m1 * v1 + m2 * v2 = m * v
1 * 1 + 5 * 0 = (1 + 5) * v
1 = 6 * v
v = 1/6 m/s
So the final speed of the 6 kg chunk will travel at 0.167 m/s</span>
