Question

A stone is dropped vertically downward from a certain height. If it reaches the ground after 5 seconds, find the height from which it was dropped.

Answer 1

The height from which the stone was dropped can be calculated using the formula:
`\( h = (1)/(2)gt^2 \)`, where h is the height, g is the acceleration due to gravity
`(approximately \( 9.81 \, \text{m/s}^2 \))`, and t is the time taken (5 seconds in this case).

Step-by-step explanation:

The height from which the stone was dropped can be determined using the equation for uniformly accelerated motion under gravity, given as
`\( h = (1)/(2)gt^2 \)`. Plugging in the values, where g is the acceleration due to gravity
`(approximately \( 9.81 \, \text{m/s}^2 \))` and t is the time taken (5 seconds), the height can be calculated.

This formula derives from the kinematic equation that relates the distance traveled by an object in free fall to the time it takes and the acceleration due to gravity. Rearranging the equation
`\( h = (1)/(2)gt^2 \)` allows us to solve for the initial height.

Given that the stone was dropped vertically downward, the initial velocity is zero. Therefore, the equation
`\( h = (1)/(2)gt^2 \)` represents the distance traveled due to the acceleration of gravity over time, giving us the height from which the stone was dropped.

In this case, with a time of 5 seconds, applying the formula yields the height from which the stone was dropped, providing a straightforward approach to determining the initial height based on the time taken for the stone to reach the ground.