Answer:
[tex]0\; {\rm J}[/tex].
Explanation:
The speed of an object is a scalar quantity and is independent of the direction in which the object is moving.
The kinetic energy of an object depends only on the mass and speed of this object. If an object of mass [tex]m[/tex] is moving at a speed of [tex]v[/tex], the kinetic energy of this object will be [tex](1/2)\, m\, v^{2}[/tex].
As a result, as long as the speed of the object stays unchanged, changes in the direction of motion of the object will not affect the kinetic energy of the object.
In this question, the speed of this ball was initially [tex]1.72\; {\rm m\cdot s^{-1}}[/tex]. The kinetic energy of this object was initially [tex](1/2)\, (0.140\; {\rm kg})\, (1.72\; {\rm m\cdot s^{-1}})^{2} \approx 0.207\; {\rm J}[/tex].
The speed of this ball stays the same after the ball bounces back from the wall: [tex]1.72\; {\rm m\cdot s^{-1}}\![/tex]. As a result, the kinetic energy of this object would still be [tex](1/2)\, (0.140\; {\rm kg})\, (1.72\; {\rm m\cdot s^{-1}})^{2} \approx 0.207\; {\rm J}[/tex].
As a result, the change in the kinetic energy of this object would be [tex]0.207\; {\rm J} - 0.207\; {\rm J} = 0\; {\rm J}[/tex].