Final answer:
The maximum height reached by the ball is approximately 9.96 meters. The closest option to this value is option c) 305m.
Step-by-step explanation:
To find the maximum height reached by the ball, we need to consider the vertical motion of the ball. The initial velocity of the ball is given by the upward velocity of the balloon, which is 14 m/s. The acceleration due to gravity is -9.8 m/s^2 (negative because it acts downwards). Using the equations of motion, we can calculate the maximum height.
We can use the formula: final velocity^2 = initial velocity^2 + 2 * acceleration * displacement. At the maximum height, the final velocity is 0 m/s. Plugging in the values, we get: 0 = (14)^2 + 2 * (-9.8) * displacement. Solving for the displacement, we find: displacement = (14)^2 / (2 * 9.8) = 9.96 m.
Therefore, the maximum height reached by the ball is approximately 9.96 meters. The closest option to this value is option c) 305m.