Question

Energy conservation with conservative forces: Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct?A) At their highest point, the acceleration of each ball is instantaneously equal tozero because they stop for an instant.B) The balls will reach the same height because they have the same mass and thesame acceleration.C) At its highest point, ball B will have twice as much gravitational potential energyas ball A because it started out moving twice as fast.D) Ball B will go twice as high as ball A because it had twice the initial speed.E) Ball B will go four times as high as ball A because it had four times the initialkinetic energy.

Answer 1

Answer:

E) True.   Ball B will go four times as high as ball A because it had four times the initial kinetic energ

Explanation:

To answer the final statements, let's pose the solution of the exercise

Energy is conserved

Initial

          Em₀ = K

          Em₀ = ½ m v²

Final

         Emf = U = mg h

         Em₀ = emf

        ½ m v² = mgh

        h = v² / 2g

For ball A

         h_A = v² / 2g

For ball B

        h_B = (2v)² / 2g

        h_B = 4 (v² / 2g) = 4 h_A

Let's review the claims

A) False. The neck acceleration is zero, it has the value of the acceleration of gravity

B) False. Ball B goes higher

C) False  has 4 times the gravitational potential energy than ball A

D) False.  It goes 4 times higher

E) True.