A 124 kg balloon carrying a 22 kg basket is descending with a constant downward velocity of 20 m/s. A 1 kg stone is thrown from the basket with an initial velocity of 15 m/s perpendicular to the path of descent. A person below measures that it takes the stone 5 s to hit the ground. At the instant the stone hits the ground, how far is it from the balloon?

To solve this problem, we can start by calculating the acceleration of the stone using the formula: acceleration = (final velocity - initial velocity) / time. Since the stone is thrown horizontally, its initial velocity and final velocity in the vertical direction will be 0 m/s. Thus, the acceleration of the stone is 9.8 m/s2 (due to gravity).

Next, we can calculate the time it takes for the stone to hit the ground using the equation: distance = initial velocity × time + (0.5 × acceleration × time2). Plugging in the values, we get: distance = 15 m/s × 5 s + (0.5 × 9.8 m/s2 × 5 s2) = 75 m.

Since the stone was thrown horizontally, it maintains its horizontal velocity of 15 m/s. Therefore, the horizontal distance the stone travels from the balloon can be calculated using the formula: distance = velocity × time = 15 m/s × 5 s = 75 m. Therefore, the stone is 75 meters away from the balloon when it hits the ground.

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