Find the height of a hot air balloon if an object which falls from it covers 19% of the height in the last second of its fall.
To find the height of the hot air balloon, we can use the equation of motion for an object in free fall:
h = 0.5 * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and t is the time taken for the object to fall.
Given that the object covers 19% of the height in the last second of its fall, we can set up the following equation:
0.19h = 0.5 * g * (t - 1)^2
We need to solve this equation to find the value of h. Here's a step-by-step calculation to find the height of the hot air balloon:
1. Rearrange the equation:
0.19h = 0.5 * g * (t^2 - 2t + 1)
2. Divide both sides of the equation by 0.19:
h = (0.5 * g * (t^2 - 2t + 1)) / 0.19
3. Simplify the equation:
h = 2.63 * (t^2 - 2t + 1)
Now we have an equation to calculate the height of the hot air balloon based on the time it takes for the object to fall. To find the specific height, we need to know the time it takes for the object to hit the ground or any other reference point.
Please provide the time the object takes to fall, and we can calculate the height of the hot air balloon based on that information.