Billy drops a ball from a height of 1 m. The ball bounces back to a height of 0.8 m, then bounces again to a height of 0.5 m, and bounces once more to a height of 0.2 m before

coming to a rest. Up is the positive direction. What are the total displacement of the ball and

the total distance traveled by the ball?

The displacement is  

The distance  is  

Explanation:

From  the question we are told that

    The height from which the ball is dropped is  

    The height attained at  the first bounce is  

    The height attained at  the second bounce is  

    The height attained at  the third bounce is

Note  : When calculating displacement we consider the direction of motion

Generally given that upward is positive  the total displacement of the ball is mathematically represented as

Here the 0 show that there was no bounce back to the point where Billy released the ball  

=>          

Generally the distance covered by the ball is mathematically represented as  

The 2 shows that the ball traveled the height two times

=>          

vapour or gas assuming atmospheriv pressure