How to Calculate the Velocity of an Object Under Gravitational Acceleration

A student drops a ball from the top of a tower with a height of 19.6m. The velocity with which the ball hits the ground is:

A) 9.8 m/sec.

B) 12/8 m/sec.

C) 19.6 m/sec.

D) 39.2 m/sec.

Final answer: The ball, dropped from a height of 19.6m, hits the ground with a velocity of approximately 19.6 m/s, calculated using the formula for an object under gravitational acceleration.

When calculating the velocity of an object under gravitational acceleration, it is important to understand the key formula involved. The formula to determine the velocity of an object falling under the influence of gravity is v = √2gh.

In this formula:

• v represents the final velocity of the object,
• g is the acceleration due to gravity (which is approximately 9.8 m/s² on Earth), and
• h is the height from which the object is dropped.

By substituting the values of g and h into the formula, we can calculate the final velocity of the object when it reaches the ground after falling from a certain height.

In the given question where a ball is dropped from a height of 19.6m, the final velocity can be calculated as follows:

v = √2 * 9.8 * 19.6

v = √(2 * 9.8 * 19.6)

v = √(382.72)

v ≈ 19.6 m/s

Therefore, the ball hits the ground with a velocity of approximately 19.6 m/s (option C in the given choices).

Understanding and applying this formula can help in calculating the velocity of objects falling under gravitational acceleration, providing valuable insights into the motion of objects in free fall.