To determine the acceleration due to gravity on the distant planet, we can use the kinematic equation for an object thrown upwards:
h = ut - (1/2)gt^2
where:
h is the maximum height reached by the rock,
u is the initial velocity of the rock (13.5 m/s),
g is the acceleration due to gravity on the planet (what we want to find),
and t is the time taken for the rock to reach its maximum height and return to the astronaut's hand (21.8 s).
Since the rock starts and ends at the same height (in the astronaut's hand), the maximum height reached is zero. Plugging in the given values, we get:
0 = (13.5 m/s) * (21.8 s) - (1/2)g * (21.8 s)^2
Simplifying this equation, we get:
(13.5 m/s) * (21.8 s) = (1/2)g * (21.8 s)^2
Rearranging the equation to solve for g, we have:
g = (2 * (13.5 m/s) * (21.8 s)) / (21.8 s)^2
Plugging in the values and performing the calculations, we find that the acceleration due to gravity on the distant planet is approximately 13.5 m/s^2 in the direction opposite to the direction of the throw.