How Fast Does a Ball Travel When Dropped from a Height?

[Physics-Pure]

Homework Statement

A ball of mass 0.163 kg is dropped from a
height 1.89 m above the ground.
The acceleration of gravity is 9.8 m/s^2
Neglecting air resistance, determine the
speed of the ball when it is at a height 0.997 m
above the ground.
Answer in units of m/s

Homework Equations

Gravitational Energy = Kinetic Energy

Mass x Acceleration From Gravity x Height = 1/2 (mass)x(velocity)^2

Acceleration From Gravity x Height = 1/2 (velocity)^2 [mass cancels]

The Attempt at a Solution

(9.8 m/s^2) x (1.89m) = 1/2 (velocity)^2

Velocity^2 = 2[(9.8 m/s^2) x (1.89m)]

Velocity = ~6.08 m/s

 

[voko]

Gravitational Energy = Kinetic Energy

Mass x Acceleration From Gravity x Height = 1/2 (mass)x(velocity)^2

This is correct only when one kind of energy is converted entirely into another. Which is not the case in this problem. What equation should you really use?

 

[Physics-Pure]

Vf = sqrt 2a delta y?

 

[azizlwl]

Homework Statement

A ball of mass 0.163 kg is dropped from a
height 1.89 m above the ground.
The acceleration of gravity is 9.8 m/s^2
Neglecting air resistance, determine the
speed of the ball when it is at a height 0.997 m
above the ground.
Answer in units of m/s
[]

Check the height.

 

[Nickie]

I can confirm that your calculations and answer are correct. The velocity of the ball at a height of 0.997 m above the ground is approximately 6.08 m/s. This is due to the conservation of energy, where the gravitational potential energy at the initial height is converted into kinetic energy as the ball falls. Neglecting air resistance, the acceleration from gravity remains constant and can be used to calculate the velocity at any point during the fall. It is important to note that in real-world scenarios, air resistance would affect the velocity of the falling object.