A German U2 rocket from the Second World War had a range of 300 km, reaching a maximum height of 100 km. Determine the rocket's maximum initial velocity.
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 = 100 and
......d = V^2(sin2µ)/g = 300.
Solve for V^2, equate the results and solve for µ and then V.
65
65 is not the answer dont use it
To determine the rocket's maximum initial velocity, we can use the principles of projectile motion.
The range of a projectile is given by the equation:
Range = (Velocity^2 * sin(2θ)) / g
Where:
- Range is the horizontal distance covered by the projectile
- Velocity is the initial velocity of the projectile
- θ is the launch angle
- g is the acceleration due to gravity (approximately 9.8 m/s²)
In this case, the range is given as 300 km, which is equal to 300,000 meters. We can assume that the launch angle θ is 45 degrees (as it would result in the maximum range for a given initial velocity).
Let's rearrange the equation to solve for the initial velocity:
Velocity^2 = (Range * g) / sin(2θ)
Substituting the given values:
Velocity^2 = (300,000 * 9.8) / sin(2 * 45)
sin(2 * 45) = sin(90) = 1
Velocity^2 = (300,000 * 9.8) / 1
Velocity^2 = 2,940,000
Taking the square root of both sides:
Velocity = √2,940,000
Velocity ≈ 1713.625 m/s
Therefore, the rocket's maximum initial velocity is approximately 1713.625 m/s.