Short projectile motion question

A German rocket from the second world war had a range of 3000meters reaching a maximum height of 1000meters.
Determine the rockets maximum velocity

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Vertical height h = V^2(sin^µ)/2g.

Horizontal distance = d = V^2(sin2µ)/g.
h = height, meters V = initial launch velocity, m/s, g = acceleration due to gravity, m/s^2s and µ = the elevation angle of the rocket measured from the horizontal to the launch directiion.

Thus, h = V^2(sin^2µ)/2g = 1000 and
......d = V^2(sin2µ)/g = 3000.

Solve for V^2, equate the results and solve for µ and then V.

Ignoring atmospheric drag and the influence of gravity.

To determine the rocket's maximum velocity during its flight, you need to understand the concept of projectile motion. Projectile motion involves two components: horizontal motion and vertical motion. The horizontal motion remains constant throughout the entire flight, while the vertical motion is affected by gravity.

In this case, you are given the range and maximum height of the rocket. The range refers to the horizontal distance the rocket travels, while the maximum height represents the highest point it reaches vertically.

To find the maximum velocity, you can use the following equation for projectile motion:

v = sqrt(2 * g * h)

Where:
- v represents the initial velocity of the rocket (maximum velocity)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the maximum height reached by the rocket

Using the given values, you can substitute them into the equation to calculate the rocket's maximum velocity:

v = sqrt(2 * 9.8 * 1000)
v = sqrt(19600)
v ≈ 140 m/s

Therefore, the rocket's maximum velocity is approximately 140 m/s.