Calculating Distance Traveled by a Freely Falling Body in the Last 2 Seconds of a 5-Second Fall

When a body falls freely under the influence of gravity, its motion can be described using the equations of motion. This article will explain how to calculate the distance traveled by a freely falling body during the last two seconds of a 5-second fall, using the equations of constant acceleration due to gravity.

The Equations of Motion

The standard equations of motion under constant acceleration ( g ) (acceleration due to gravity) are:

Equation for Total Distance Fallen in a Given Time ( s frac{1}{2}gt^2 )

Where:

( s ) is the distance travelled (in meters) ( g ) is the acceleration due to gravity (( 9.81 , text{m/s}^2 )) ( t ) is the time in seconds

Calculating the Total Distance Fallen in 5 Seconds

First, we calculate the total distance travelled in 5 seconds:

s  frac{1}{2} times 9.81 times 5^2  frac{1}{2} times 9.81 times 25  122.625 , text{m}

Distance Fallen in the First 3 Seconds

To find the distance fallen in the first 3 seconds, we use the same formula:

s_3  frac{1}{2} times 9.81 times 3^2  frac{1}{2} times 9.81 times 9  44.145 , text{m}

Distance Traveled in the Last 2 Seconds

Now, we subtract the distance fallen in the first 3 seconds from the total distance travelled in 5 seconds to find the distance travelled in the last 2 seconds:

Distance in last 2 seconds  s - s_3  122.625 - 44.145  78.48 , text{m}

Therefore, the distance travelled by the freely falling body in the last 2 seconds is approximately ( boxed{78.48} ) meters.

Additional Notes on Calculation Methods

Alternatively, you can calculate the height covered using the following steps:

Height Covered in 5 Seconds ( h_5 )

h_5  frac{1}{2} times g times 5^2  frac{1}{2} times 9.81 times 25  122.625 , text{m}

Height Covered in 3 Seconds ( h_3 )

h_3  frac{1}{2} times g times 3^2  frac{1}{2} times 9.81 times 9  44.145 , text{m}

Subtracting these values:

Height covered in the last 2 seconds  h_5 - h_3  122.625 - 44.145  78.48 , text{m}

Conclusion

By understanding and applying the equations of motion, you can accurately calculate the distance traveled by a freely falling body at any point in time. This method is particularly useful for physics calculations and solving related problems in mechanics.