Question

On the moon, all free-fall distance functions are of the form s(t) = 0.81t², where t is in seconds and s is in meters. An object is dropped from a height of 250 meters above the moon. After 8 sec,

a) How far has the object fallen?

Answer 1

After 8 seconds of free-fall on the Moon, an object has fallen 51.84 meters, as calculated using the moon's free-fall distance function s(t) = 0.81t².

Step-by-step explanation:

An object dropped on the Moon is subject to lunar gravity and follows the free-fall distance function s(t) = 0.81t², where t is time in seconds, and s is the distance fallen in meters. To find out how far the object has fallen after 8 seconds, we simply plug the time into our formula:

s(8) = 0.81 × 8²

Caring out the computation:

s(8) = 0.81 × 64 = 51.84 meters.

The object has therefore fallen 51.84 meters after 8 seconds. In answering this student's question, we assumed that the object was dropped with an initial velocity of zero and the acceleration due to gravity on the Moon has already been accounted for in the given free-fall distance function.