Launch Velocity Calculator

Formula

To calculate the Launch Velocity (\(V\)):

\[ V = X \times \sqrt{\frac{g}{2H}} \]

Where:

\(V\) is the Launch Velocity (m/s)
\(X\) is the Change in X-direction (m)
\(H\) is the Maximum Height (m)
\(g\) is the Acceleration due to Gravity (m/s²)

What is Launch Velocity?

Launch velocity describes the magnitude of the speed of an object or projectile being launched from the ground. It is the initial velocity needed for the projectile to reach its maximum height and cover the horizontal distance.

Example Calculation 1

Let's assume the following values:

Change in X-direction (\(X\)) = 50 m
Maximum Height (\(H\)) = 20 m
Acceleration due to Gravity (\(g\)) = 9.81 m/s²

Using the formula:

\[ V = 50 \times \sqrt{\frac{9.81}{2 \times 20}} = 50 \times \sqrt{\frac{9.81}{40}} = 50 \times \sqrt{0.24525} \approx 50 \times 0.4952 \approx 24.76 \]

The Launch Velocity is approximately 24.76 m/s.

Example Calculation 2

Let's assume the following values:

Change in X-direction (\(X\)) = 30 m
Maximum Height (\(H\)) = 10 m
Acceleration due to Gravity (\(g\)) = 9.81 m/s²

Using the formula:

\[ V = 30 \times \sqrt{\frac{9.81}{2 \times 10}} = 30 \times \sqrt{\frac{9.81}{20}} = 30 \times \sqrt{0.4905} \approx 30 \times 0.7004 \approx 21.01 \]

The Launch Velocity is approximately 21.01 m/s.