Question

Find the velocity with which the ball strikes the ground?

Answer 1

To calculate the velocity with which the ball will strike the ground use Newton's Third equation if motion
v²= u²+ 2gh
v= velocity with which ball strikes the ground
u = initial velocity
g= acceleration due to gravity
h= total height

Answer 2

Dear student,

Let us assume the following data for concluding a formula/derivation of the velocity with which a ball strikes a ground.

There has to be a ball any mass 'm', it has to be at a certain height above the ground 'H', it has to be projected on the ground/ dropped to strike the ground with some initial velocity/ no initial velocity.

Case 1: If the object is dropped from some height and we were to find the final velocity of the ball with which it strikes the ground.

According to the work-energy theorem, work done by all the forces is equal to the change in the kinetic energy.

Here,            Wgravity = Δ K.E.

                      mgH = 1/2 m(Vf² - Vi²)

                      mgH = 1/2 m(Vf² - 0²)

                         2gh = Vf²

                          Vf² = √2gh

Therefore, the velocity with which the ball strikes the ground in this case is √2gh.

Case 2: If the object is to be projected with some initial velocity and we were to find the final velocity of the ball with which it strikes the ground.

Again, according to the work-energy theorem, work done by all the forces is equal to the change in the kinetic energy.

Here,            Wgravity = Δ K.E.  

                      mgH = 1/2 m(Vf² - Vi²)

                         gH = 1/2 (Vf² - u²)  

[let the initial velocity of projectile be u]

                       2gh = Vf² - u²

                         Vf² = 2gh + u²

                         Vf = √u² + 2gh

Therefore, the velocity with which the ball strikes the ground in this case is √u² + 2gh.

Conclusion: Possible values of velocity with which the ball strikes the ground are:

If projected, then final velocity = √u² + 2gh

If dropped, then final velocity = √2gh