Muzzle Speed of Gun with 24.5 km Range

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To find the muzzle speed of a gun with a maximum range of 24.5 km, the equation R = V0^2 sin(2*angle)/g is used, where R is the range, V0 is the muzzle speed, and g is the acceleration due to gravity. A participant questions how to determine the angle for maximum range and seeks clarification on a previous calculation involving a projectile fired at 840 m/s at a 60-degree angle, which incorrectly calculated the time to reach 21 km as 25 seconds instead of the correct 50 seconds. The discussion emphasizes the importance of the launch angle, noting that the optimal angle for maximum range is 45 degrees. Understanding the relationship between angle and range is crucial for accurate projectile motion calculations. The conversation highlights common pitfalls in physics problems related to projectile motion.
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Homework Statement


Find the muzzle speed of a gun whose maximum range is 24.5 km.


Homework Equations


R = V02sin2angle/g


The Attempt at a Solution


How do I find the angle?

Also can you check what I did wrong in this one?
A projectile is fired at a speed of 840 /sec at an angle of 60 degree. How long will it take to get 21 km downrange?
change in X = V1t
21,000/840 = t
t=25 sec
But the right answer is 50 s
 
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The angle for maximum range should be obvious - think what happens if you shoot straight up or straight horizontal?
 

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