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What is the maximum range of a shell projected across horizontal ground from a gun with an initial speed of 300 m s-1? What will its speed be at the highest point of its trajectory? (Ignore air resistance.)

The questoin above, i have tried but can't get it. The answers are 9000 m; 212 m s-1. Im confused as the question gives no height above the ground, secondly. If the shell is being projected horizontally then doesnt that mean the highest point will be the muzzle of the gun. So the max speed will be 300 still ?

Just not sure how to approach this. Some guidence will be greatly appriecided !

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  • $\begingroup$ Im assuming launch angle is taken to be 45 degrees , with that you can achieve your answer approximately $\endgroup$
    – Naveen V
    Apr 13, 2023 at 14:56

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This question is asking for the maximum range trajectory as a function of the initial angle relative of the projectile's motion to the ground. If the projectile is launched vertically, it will end up at its launch point. If launched exactly horizontally, it will strike the ground immediately (it starts at ground level). So there is some intermediate angle that maximizes how far the projectile gets away from it's launch point.

The horizontal stipulation is in regards to the ground -- assume the ground is flat even though the Earth is spherical.

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