A ball is launched upward at 14 m/s from a platform 30 m high. Find the maximum height the ball will reach and how long it will take.

The ball will reach a maximum height of 39.993 meters after 1.428 seconds.

Step-by-step explanation:

Let suppose that no non-conservative forces acts on the ball during its motion, then we can determine the maximum height reached by the Principle of Energy Conservation, which states that:

(1)

Where:

, - Initial and final translational kinetic energies, measured in joules.

, - Initial and final gravitational potential energies, measured in joules.

By definition of translational kinetic energy and gravitational potential energy we expand and simplify the expression above:

(2)

Where:

- Mass of the ball, measured in kilograms.

- Gravitational acceleration, measured in meters per square second.

, - Initial and final speed of the ball, measured in meters per second.

, - Initial and final heights of the ball, measured in meters.

The final height of the ball is determined by the following formula:

(3)

If we know that , , and , the maximum height that the ball will reach is:

The ball will reach a maximum height of 39.993 meters.

Given the absence of non-conservative forces, the ball exhibits a free fall. The time needed for the ball to reach its maximum height is computed from the following kinematic formula:

(4)

If we know that , and , then:

The ball will take 1.428 seconds to reach its maximum height.

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