Initial Height Calculator

Formula

The formula to calculate the initial height is:

\[ H_i = H_f + V \times t + 0.5 \times g \times t^2 \]

Where:

\(H_i\) is the initial height (meters)
\(H_f\) is the final height (meters)
\(V\) is the velocity (meters per second)
\(t\) is the time (seconds)
\(g\) is the acceleration due to gravity (9.80665 m/s^2)

What is Initial Height?

Initial height is the height from which an object starts its motion when dropped or thrown vertically upwards or downwards. It is an important parameter in kinematics for determining the motion of objects under the influence of gravity.

Initial Height Example

Let's assume the following:

Final Height (\(H_f\)): 10 meters
Velocity (\(V\)): 5 meters per second
Time (\(t\)): 2 seconds

Step 1: Calculate the initial height:

\[ H_i = 10 + (5 \times 2) + 0.5 \times 9.80665 \times 2^2 \]

\[ H_i = 10 + 10 + 0.5 \times 9.80665 \times 4 \]

\[ H_i = 10 + 10 + 19.6133 = 39.6133 \, \text{meters} \]

Therefore, the initial height is approximately 39.61 meters.