Question

# You throw a rock with an initial horizontal velocity and it hits the ground at x...

You throw a rock with an initial horizontal velocity and it hits the ground at x meters away from your feet. What if: (a) You throw the same stone with the same initial conditions but instead you do this on a another planet with a mass 4 times the mass of the earth. With what factor will x change? (b) You throw the same stone with the same initial conditions but instead you do this on a another planet with a radius 7 times the radius of the earth. With what factor will x change?

Let the height from which rock is thrown is h

$g = \frac{GM}{R^2}$

$t = \sqrt{\frac{2h}{g}}$

$x = u_x t = u_x \sqrt {\frac{2h}{g}}$

Now , when thrown on other planet .

$g' = \frac{GM'}{R'^2}$

a) M' = 4M

$g' = \frac{4GM}{R^2} = 4g$

$x' = u_x t = u_x \sqrt {\frac{2h}{g'}} = u_x \sqrt {\frac{2h}{4g}}$

$x' = \frac{x}{2}$

b) . R' = 7R

$g' = \frac{GM}{49R^2} = \frac{g}{49}$

$x' = u_x t = u_x \sqrt {\frac{2h}{g'}} = u_x \sqrt {\frac{98h}{g}}$

$x' = 7x$

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