What is the distance fallen by a freely falling object after 4 seconds?

To determine the distance fallen by a freely falling object after 4 seconds, we can use the formula for the distance of an object in free fall, which is given by:

[ d = \frac{1}{2} g t^2 ]

In this formula, ( d ) is the distance fallen, ( g ) is the acceleration due to gravity (approximately 9.8 m/s² on the surface of the Earth), and ( t ) is the time in seconds.

Substituting the values into the equation for a time of 4 seconds:

1. Calculate ( g \cdot t^2 ): [ g \cdot t^2 = 9.8 , \text{m/s}^2 \cdot (4 , \text{s})^2 = 9.8 \cdot 16 = 156.8 , \text{m} ]

2. Now, apply the formula: [ d = \frac{1}{2} \cdot 156.8 , \text{m} = 78.4 , \text{m} ]

Rounding 78.4 meters to the nearest