A stone is dropped vertically from the top of a tower of height 40 meters. At the same time, a gun is aimed directly at the stone from the ground at a horizontal distance of 30 meters from the base of the tower and fired if the bullet from the gun is to hit the stone before it reaches the ground. The minimum velocity of the bullet must be approximately how much?

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We have a projectile motion problem. A stone is dropped vertically from the top of a 40-meter tower. At the same time, a gun positioned 30 meters horizontally from the tower base fires a bullet aimed directly at the stone. We need to find the minimum velocity required for the bullet to hit the stone before it reaches the ground. Let's set up a coordinate system to solve this problem. We place the gun at the origin, coordinates zero zero. The base of the tower is at coordinates thirty zero, and the stone starts at coordinates thirty forty. The bullet is aimed directly at the stone's initial position. The angle of elevation theta satisfies tangent theta equals forty over thirty, which equals four thirds. From this, we can calculate that sine theta equals four fifths and cosine theta equals three fifths.