What is the Maximum Range of a Fired Shot from a Launcher?

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The discussion centers on calculating the maximum range of a projectile launched at an optimal angle. A ball weighing 30kg is fired to a height of 300m, leading to a calculated initial velocity of 76.68 m/s when fired straight up. The maximum range is achieved by launching at a 45° angle, resulting in a horizontal velocity component of 54.22 m/s. Using the range formula, the maximum range is determined to be 600m, confirming that the initial speed remains consistent regardless of the launch angle. The calculations and understanding of the projectile motion principles appear to be correct.
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Homework Statement



A launcher fires a ball that weighs 30kg straight up to a height of 300m. What is the maximum range of the ball could be fired at?

Homework Equations


V^2 = V^2-2(a)(d)
R = ( V02 Sin2θ ) / g

The Attempt at a Solution



To find the maximum range i know that it has to be fired at a 45° angle.
It is in our energy and momentum etc. unit, practice so I am guessing equations relevant to that is what i must use.
I used this equation to find the Velocity when fired straight up. Which i got 76.68 m/s. Which if i drew a triangle to show the projectory, would be my height. I then used 76.68SIN(45°) to get 54.22 m/s. Which is my x & y velocity. Then i used the range formula to get 300 m.
Is anything wrong with my work, shouldn't it be a different answer than 300m.
 
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What is the initial speed?
What is the expression for the maximum range?
You don't really need to calculate the components of the velocity if you already know the formula for the range.
 
So the initial speed no matter the angle you fire at will all be the same?
 
I believe i ended up getting it. answer 600m
 
Yes, this looks OK.
 
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