Question

Sharon drops a rubber ball from a height of 160 feet. Every bouce sends the ball half as high as it was before. What is the total vertical (up and down) distance the ball has traveled, from the moment it is dropped to the moment it hits the floor for the fourth time?

Answer 1

First drop to the ground, it travels 160 ft

Then it goes up  1/2 * 160 = 80 ft  after hitting ground for first time.

then distances travelled up and down until fourth hit are:-

80,  (2nd hit) 40 , 40 (3rd hit)  , 20 , 20 (4th hit)

So answer is  160 + 2(80) + 2(40) + 2(20)

=  440 feet   (answer)

Answer 2

The total vertical distance traveled by the ball is 440 feet.

How to calculate the distance travelled by the rubber ball after successive collision ?

For the first hit, the ball is dropped from a height of 160 feet.

It is also given that for every bounce the ball travels half the distance it had travelled in the previous bounce.

∵ For second (2nd) bounce, height reached

= 1/2*160 = 80 feet

Similarly, for third (3rd) bounce, height reached

= 1/2*80 = 40 feet

And finally for fourth (4th) bounce, height reached

= 1/2*40 = 20 feet

As we have to calculate both up and down vertical height ,

For 2nd bounce -

= 80*2 = 160 feet

For 3rd bounce -

= 40*2 =  80 feet

For 4th bounce -

= 20*2 =  40 feet

∴ The total vertical height traveled by the ball is

= (160 + 160 + 80 + 40) feet = 440 feet

Thus the total distance traveled by the ball is 440 feet.

To learn more about concept of distance travelled, refer:

https://brainly.com/question/13104701

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