Answer:
B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy.
Explanation:
The complete question is
Two identical balls are thrown directly upward, ball A at speed v and boll B at speed 2v. and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.
According to conservation of energy, the mechanical energy of a ball thrown up is equal to the sum of the potential energy and the kinetic energy. At its highest point, all the mechanical energy will be equal to the potential energy. At the instant when it was thrown, all the mechanical energy is proportional to its kinetic energy, which will be proportional to the potential energy at the highest point. Also, potential energy is proportional to the maximum height reached.
We know that the kinetic energy is given as [tex]\frac{1}{2}mv^{2}[/tex]
where
m is the mass of the balls, which is the same for both ball,
and v is the velocity.
We can see that the kinetic energy is proportional to the square of the initial velocity with which the ball is thrown.
For the ball A thrown with velocity v, the kinetic energy is proportional to [tex]v^{2}[/tex],
and for the ball B with velocity 2v, kinetic energy is proportional to [tex]4v^{2}[/tex]
comparing the two, we'll see that the ball B will had 4 times the energy of ball A. Therefore ball B will go four times as high as ball A because it had four times the initial kinetic energy
