Volcano in mars ejects rocks. Straight line motion

[Toranc3]

Homework Statement

A certain volcano on Earth can eject rocks vertically to a maximum height .

Part A: How high (in terms of H ) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s^2 , and you can neglect air resistance on both planets.

Homework Equations

y=yo + vo*t + 1/2 *g*t^(2)

vy=vo + g*t

The Attempt at a Solution

y=yo + vo*t - 1/2 *g*t^(2)


vy=vo + g*t
0=vo-g(mars)*t

t=vo/g
substitute this in y=yo + vo*t - 1/2 *g*t^(2)

to get y=1/2 * vo^(2)/g

After this I am stuck. The answer is 2.64H or 2.64Y

 

[Dick]

Homework Statement

A certain volcano on Earth can eject rocks vertically to a maximum height .

Part A: How high (in terms of H ) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s^2 , and you can neglect air resistance on both planets.

Homework Equations

y=yo + vo*t + 1/2 *g*t^(2)

vy=vo + g*t

The Attempt at a Solution

y=yo + vo*t - 1/2 *g*t^(2)


vy=vo + g*t
0=vo-g(mars)*t

t=vo/g
substitute this in y=yo + vo*t - 1/2 *g*t^(2)

to get y=1/2 * vo^(2)/g

After this I am stuck. The answer is 2.64H or 2.64Y

g on Earth is 9.8m/s^2. What's the ratio of y=1/2 * vo^(2)/g between Mars and Earth?

 

[Toranc3]

g on Earth is 9.8m/s^2. What's the ratio of y=1/2 * vo^(2)/g between Mars and Earth?

Ah I see now thanks. However how do you know when to take the ratio? I did not even think about that.

 

[Dick]

Ah I see now thanks. However how do you know when to take the ratio? I did not even think about that.

The height on Earth is H=(1/2)v0^2/(9.8m/s^2). The height on Mars will be (1/2)v0^2/(3.71m/s^2). If you divide the two then everything will cancel except for the ratio of the two values of g.

 

[Toranc3]

The height on Earth is H=(1/2)v0^2/(9.8m/s^2). The height on Mars will be (1/2)v0^2/(3.71m/s^2). If you divide the two then everything will cancel except for the ratio of the two values of g.

Got it and thank you.