Question

On a manned orbital mission to a planet in the far, far reaches of the galaxy, the brave astronauts observe ageyser spouting from the surface of the planet. These astronauts have measured the water to emerge from theseyser with an initial speed of 15.00 m/sec. Further measurements confirm that the gravitational accelerationon the surface of the planet to be 8.20 m/s2. How high does the water spew up from the geyser in meters?

Answer 1

13.72 m

Step-by-step explanation:

To know how high will the water spews up, we will use the following equation:

`v^2_f=v^2_0+2a(\Delta x)`

Where vf is the final velocity, v0 is the initial velocity, a is the acceleration of gravity and Δx is the height of the water.

When the water is at the highest point, the final velocity is 0m/s. So, replacing vf by 0 m/s, v0 by 15 m/s, and a by -8.20 m/s², we get:

`0^2=15^2+2(-8.2)(\Delta x)`

Then, solving for Δx, we get:

`\begin{gathered} 0=225-16.4\Delta x \\ 16.4\Delta x=225 \\ \Delta x=(225)/(16.4) \\ \Delta x=13.72\text{ m} \end{gathered}`

So, the answer is 13.72 m