Question

a mars lander weighs 767pounds on earth but only 291 pounds on mars it the mars rover weighs 155 pounds on mars, how much does it weigh on earth?

Answer 1

I got approximately `409` pounds.

Explanation:

We can use ratios here, let the Mars rover weigh `x` pounds on Earth, then we got

`767/291=x/155`

or

`x=767/291*155`

`~~409` pounds to the nearest whole number

Answer 2

I'll leave you to solve the problem yourself.

Explanation:

Weight is simply the force applied on a mass due to gravity. The mass of the Mars Lander in this problem is posited to be 767lbs on earth. We know that the gravitational acceleration on earth is approximately 32.2 ft/s^2 at sea level, which we will use to get an approximate solution to this question. The force on a mass due to gravity is determinable by Newton’s universal law of gravitation:

`F = (G*m_1 * m_2 )/ r_2` ------------- eq. 1

G is a gravitational constant
m_1, m_2 are the masses of two masses of interest, such as a planetary body and a mass on it's surface.
r_2 is the distance between the two masses, such as the radius of a planetary body.

On earth, we know that....

`(G*m_(earth))/r_(earth) = g_(earth) = 32.2 (ft)/s^2` ------------- eq. 2

From the problem, we are told that the solution to this equation on earth for the Mars Lander is 767lbs of force. If we plug this known force and eq. 2 into the general equation (eq. 1), we have:

`767 = 32.2 (ft)/s^2 *m_2`

This allows us to solve for the mass of the Mars Lander (m_2). Knowing the mass of the Mars Lander and the resultant gravitational force (i.e. weight) on the surface of Mars of 291lbs force, we can then calculate the gravitational constant on Mars' surface.

`291 = g_(mars) * m_2`

We now know the quantitative approximation for the gravitational constant on Mars, and thus can calculate the weight of any known mass on the surface of Mars. Conversely, we can calculate the mass of any known weight on the surface of Mars.