Volcano in mars ejects rocks. Straight line motion

• Toranc3
In summary, the question is asking how high rocks ejected from a volcano on Mars would go if they were ejected with the same initial velocity as a volcano on Earth. The solution involves using the equations for displacement and velocity, and taking into account the different values for gravity on each planet. The final answer is 2.64 times the height on Earth, or 2.64H.
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

Toranc3 said:

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?

Dick said:
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.

Toranc3 said:
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.

Dick said:
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.

1. How do volcanoes form on Mars?

Volcanoes on Mars are formed by the movement of molten rock, or magma, beneath the surface. As the magma rises towards the surface, it can create cracks and weak spots in the Martian crust, eventually erupting in the form of a volcano.

2. Is the volcanic activity on Mars similar to that on Earth?

While the basic process of volcanic activity is similar on both Mars and Earth, there are some key differences. For example, Martian volcanoes tend to be much larger and have more gentle slopes compared to the steeper, more explosive volcanoes on Earth.

3. What kind of rocks are ejected from Martian volcanoes?

The rocks ejected from Martian volcanoes can vary in composition, but they are typically made up of basalt, a type of volcanic rock that is common on both Mars and Earth. These rocks can range in size from small pebbles to large boulders.

4. How far can rocks be ejected from a Martian volcano in a straight line?

The distance that rocks can be ejected from a Martian volcano in a straight line varies depending on the size and force of the eruption. In general, they can travel anywhere from a few meters to several kilometers away from the volcano.

5. What role does gravity play in the motion of rocks ejected from Martian volcanoes?

Gravity plays a significant role in the motion of rocks ejected from Martian volcanoes. As the rocks are propelled upwards by the force of the eruption, they will eventually be pulled back down to the surface due to the planet's gravity, resulting in a generally straight line motion.

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