Final answer:
The volcanic plume on Earth could reach a height of approximately 19.87 kilometers. On Venus, where gravity is nearly the same as on Earth, the plume would reach a similar height. Therefore, the plume would neither be significantly higher nor lower on Venus compared to Earth.
Step-by-step explanation:
The question requires calculation of the maximum height a volcanic plume could reach on Earth when thrown at a speed of 625 m/s, and to compare this height with how high the plume would rise on Venus, where gravity is almost the same as Earth's.
A) Calculate the height on Earth
To calculate the maximum height reached by the volcanic plume on Earth, we can use the kinematic equation for motion under gravity, assuming the plume goes straight up and neglecting air resistance:
vf^2 = vi^2 + 2 * a * d
Where vf is the final velocity (which will be 0 m/s at the highest point), vi is the initial velocity (625 m/s), a is the acceleration due to gravity (-9.81 m/s^2 on Earth, negative because it is in the opposite direction to the motion), and d is the distance or height (which we are trying to find).
Rearranging the formula to solve for d:
d = (vf^2 - vi^2) / (2 * a)
Substituting the known values:
d = (0 - 625^2) / (2 * -9.81)
d = 19869.53 meters or approximately 19.87 kilometers
B) Calculate the height on Venus
Since the acceleration due to gravity on Venus is nearly the same as on Earth, the plume on Venus would rise to a similar height as it does on Earth.
C) The height on Venus would be higher
This statement is incorrect based on the given information that Venus has nearly the same gravity as Earth, so the plume would not rise significantly higher or lower.
D) The height on Venus would be lower
This statement is also incorrect for the same reason given for statement C.