A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of 100 m/s at an angle of 30° above the horizontal. The horizontal distance between the cannon and the target is: (Acceleration due to gravity = 10 m/s²)

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We have a projectile motion problem. A cannon is placed on a cliff 375 meters high. It fires a cannonball with initial velocity 100 meters per second at an angle of 30 degrees above horizontal. We need to find the horizontal distance from the cannon to where the cannonball hits the ground. First, we identify the given parameters and break down the initial velocity into components. The horizontal component is v₀ₓ equals 100 times cosine of 30 degrees, which equals 50 root 3 meters per second. The vertical component is v₀ᵧ equals 100 times sine of 30 degrees, which equals 50 meters per second. Now we use the vertical motion equation to find the time of flight. We set y equals zero since the cannonball hits the ground, substitute our known values, and get the quadratic equation 5 t squared minus 50 t minus 375 equals zero. Solving this quadratic equation gives us t equals 15 seconds or negative 5 seconds. Since time must be positive, the time of flight is 15 seconds. Finally, we calculate the horizontal distance using the horizontal motion equation. Since there is no horizontal acceleration, the horizontal distance equals the horizontal velocity component times the time of flight. This gives us x equals 50 root 3 times 15, which equals 750 root 3 meters. This is our final answer. Let's summarize our solution. We broke the initial velocity into horizontal and vertical components, used the vertical motion equation to find the time of flight as 15 seconds, then calculated the horizontal distance using the horizontal motion equation. The final answer is 750 root 3 meters, which is approximately 1299 meters. This completes our projectile motion problem.