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A projectile is fired from a gun at an a...

A projectile is fired from a gun at an angle of `45^@` with the horizontal and with a speed of `20m//s` relative to ground. At the highest point in its flight the projectile explodes into two fragments of equal masses. One fragement, whose initial speed is zero falls vertically. How far from the gun does the other fragment land, assuming a level terrain? Take `g=10m//s^2`?

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To solve the problem step by step, we will analyze the motion of the projectile and the subsequent explosion. ### Step 1: Determine the initial velocity components The projectile is fired at an angle of \(45^\circ\) with a speed of \(20 \, \text{m/s}\). We can find the horizontal and vertical components of the initial velocity (\(U\)) using trigonometric functions: \[ U_x = U \cdot \cos(45^\circ) = 20 \cdot \frac{1}{\sqrt{2}} = 10\sqrt{2} \, \text{m/s} \] ...
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