the first active volcano observed outside the earth was discovered in 1979 on Io, one of the moons of jupiter. the volcano was observed to be ejecting material to a height of about 2.00x10^5m. given that the acceleration of gravity on Io is 1.80 m/s^2, find the initial velocity of the ejected material.
To find the initial velocity of the ejected material from the volcano on Io, we can use the equations of motion. The equation that relates the initial velocity (vi), final velocity (vf), acceleration (a), and displacement (d) is:
vf^2 = vi^2 + 2ad
In this case, we are given the following information:
- Acceleration (a) on Io is 1.80 m/s^2
- Displacement (d) is the height of the ejected material, which is 2.00x10^5 m
- We need to find the initial velocity (vi)
Since the final velocity (vf) is not mentioned, we assume it to be zero, as it is the initial velocity of the ejected material when it reaches its highest point.
Therefore, the equation becomes:
0 = vi^2 + 2ad
Rearranging the equation to solve for vi:
vi^2 = -2ad
Now we can substitute the known values and solve for vi:
vi^2 = -2 * (1.80 m/s^2) * (2.00x10^5 m)
vi^2 = -7.20x10^5 m^2/s^2
Now, taking the square root of both sides to find vi:
vi = √(-7.20x10^5 m^2/s^2)
Note that we end up with a negative square root because the initial velocity is upwards, opposite to the acceleration due to gravity.
Calculating the value using a calculator:
vi ≈ -847.71 m/s
Therefore, the initial velocity of the ejected material from the volcano on Io is approximately -847.71 m/s.