Calculating the Time for a Body to Fall from a Height of 175m

In physics, understanding the time it takes for a body to fall from a specific height is an essential concept. In this article, we'll explore how to calculate the time it takes for a body to reach the ground from a height of 175 meters, with a focus on the physical principles and the mathematical formulas involved.

The Concept and Formula

When an object is dropped from a certain height under the influence of gravity, it accelerates towards the ground at a rate of approximately 9.81 meters per second squared (m/s2) near the Earth's surface. This constant acceleration enables us to use a simple yet powerful equation to determine the time it takes for the object to reach the ground.

The governing equation for the distance traveled under constant acceleration due to gravity is:

d frac12; g t2

where:

d is the distance, 175 meters (m) g is the acceleration due to gravity, approximately 9.81 m/s2 t is the time (t)

By rearranging this formula to solve for t, we obtain:

t radic;(2d / g)

Let's apply this formula to calculate the time taken for a body to reach the ground from a height of 175 meters.

Calculation

Substituting the values:

t radic;((2 x 175) / 9.81) radic; (350 / 9.81) ≈ radic; 35.7 ≈ 5.97 seconds

Thus, it will take approximately 5.97 seconds for the body to reach the ground.

Alternative Solution

Let's consider an alternative method where the equation of motion is applied:

y vot 1/2 gt2

y is the height, 164.5 meters; vo is the initial velocity, 0 m/s; g is the acceleration due to gravity, -9.8 m/s2.

Substituting the values:

-164.5 0 1/2 (-9.8) t2

-164.5 -4.9 t2

t2 33.55

t 5.79 s

This method yields a similar time, confirming our earlier calculation.

Key Considerations

Air Resistance: In real-world applications, air resistance significantly affects the motion of the falling body, particularly at higher velocities. Ignoring air resistance simplifies the calculations but may not accurately represent the actual scenario.

For an accurate calculation, especially in practical applications, it is crucial to account for air resistance, which adds a non-zero initial velocity and modifies the acceleration due to gravity.

Key Takeaways: Understanding the formula and the physical principles enabling the calculation of the time for a body to fall from a height is fundamental in physics. The formula d frac12; g t2 is particularly useful in scenarios where air resistance is negligible.