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) 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.

Question

Quizplus · Accepted Answer

The height reached by an object thrown upward is proportional to the square of its initial velocity. Since kinetic energy is proportional to the square of the velocity ($KE = \frac{1}{2}mv^2$), doubling the initial speed ($2v$) results in four times the initial kinetic energy ($4 \times \frac{1}{2}mv^2 = 2mv^2$). This increased energy allows the object to reach a height four times greater than if it were thrown at speed $v$, assuming no air resistance and constant acceleration due to gravity.

Two Identical Balls Are Thrown Directly Upward,ball a at Speed