Question

Games in Space: On Earth, an astronaut throws a ball straight upward, and it stays in the air for a total of 3.0s before they catch it at the same height they released it. On the Moon, acceleration due to gravity is ∼ 1/6 the value on Earth. If the astronaut repeats this process on the Moon, giving the ball the same initial speed, how much time would pass before they catch it

Answer 1

if an object is thrown upwards and then it will return back into our hand then we can say for the complete motion the displacement of the object must be zero

so here we will have

$\Delta y = vt + \frac{1}{2}at^2$

here we know that

$0 = vt - \frac{1}{2}gt^2$

$t = \frac{2v}{g}$

now we will have this time t = 3 s on the surface of earth

again same experiment is performed on surface of moon with same initial speed

so the time on the surface of moon will be

$t_{moon} = \frac{2v}{g/6}$

so here we have

$t_{moon} = 6\frac{2v}{g} = 6(3) =18 s$

so it will take 18 s on moon