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

Given the same initial speed, the astronaut would catch the ball after about 7.3 seconds on the Moon because the Moon's gravitational acceleration is approximately 1/6th that of Earth.

Step-by-step explanation:

On Earth, an astronaut throws a ball straight upward and it stays in the air for a total of 3.0 seconds. On the Moon, assuming the astronaut throws the ball with the same initial speed, the duration the ball stays in the air would be longer because the Moon's gravitational acceleration is approximately 1/6th of that on Earth. We can calculate the time it takes for the ball to reach its peak height on Earth and use that to find the time on the Moon.

The total time in the air is 3.0 seconds on Earth, with 1.5 seconds to reach the highest point and another 1.5 seconds to return to the astronaut's hand. Since gravitational acceleration is 1/6th on the Moon, the ball takes √6 times longer to reach the peak and the same amount to return, making the total time 3.0 seconds × √6, which is approximately 7.3 seconds. Thus, the astronaut would catch the ball after about 7.3 seconds on the Moon.

Answer 2

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 + (1)/(2)at^2`

here we know that

`0 = vt - (1)/(2)gt^2`

`t = (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) = (2v)/(g/6)`

so here we have

`t_(moon) = 6(2v)/(g) = 6(3) =18 s`

so it will take 18 s on moon