The problem involves calculating the time it takes for a cargo box to fall to the ground from a certain height under the influence of gravity. The box is assumed to be in free fall, which means it is only subject to the force of gravity and no other forces (like air resistance).
In order to solve this problem, we need to use the equations of motion, specifically the equation for displacement under uniform acceleration. In this case, the acceleration is due to gravity, which we can approximate as 9.8 m/s².
The equation we will use is this one: d = 1/2 * g * t² where:
- d is the distance the object falls or its displacement (in this case, 1550 meters).
- g is the acceleration due to gravity (approximately 9.8 m/s²).
- t is the time it takes for the object to fall (which is what we're trying to find).
We can rearrange the equation to solve for t: t = sqrt(2d/g).
Let's plug in the values and solve:
1. Double the distance: 2 * 1550 = 3100
2. Divide that result by the acceleration due to gravity: 3100 / 9.8 = 316.3265306122
3. Finally, find the square root of that number to get the time in seconds: sqrt(316.3265306122) = 17.78557085426962
So, it would take approximately 17.79 seconds for the cargo box to fall to the ground from a height of 1550 meters.