What geometric sequence representation can you get from the bouncing ball?

What geometric sequence representation can you get from the bouncing ball?

b. In this sequence, a1=2 and r=0.8. Find the sum of the related series. Therefore, the total amount of time that the ball bounces is 10 seconds….Geometric Series: Bouncing Ball — a Ball Bounces.

Bounce	Ball Height
3	0.7(7.84)=5.488
4	0.7(5.488)=3.8416
5	0.7(3.8416)=2.68912
6	0.7(2.68912)=1.882384

What total vertical distance does the ball travel before it stops bouncing?

The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance travelled by the ball. = 6 + 9(4) = 42 feet.

What is the height of the next bounce?

The maximum height it reaches after its first bounce is 70 percent of 200 feet, or 140 feet. After the second bounce, it reaches a height of 70 percent of 140 feet, or 98 feet. In similar fashion, the ball continues to rebound to a height that is 70 percent of the highest point of the previous bounce.

Which ball bounces higher when dropped together?

When all three balls are dropped from the same height, the rubber ball will bounce the highest because it has the greatest elasticity. When the rubber ball hits the ground it gets compressed, or squished, and because it is very elastic, it quickly returns to its original shape.

How do you calculate height after bounce?

Between the first and second bounces, the height can be expressed as h = 140 − 16(t − 6.49)2, 3.54 ≤ t < 9.45. The 6.49 is when the highest point is achieved (halfway between the two bounces), and the 9.45 seconds is derived from adding 3.54 seconds to the time between the first and second bounces.

What is the relationship between drop height and bounce height?

The relationship between drop height and bounce height is only linear for small drop heights. Once a ball reaches a certain height, the bounce height will begin to level off because the ball will reach its terminal velocity.

Why does a ball bounce lower each time?

As no energy is added to the ball, the ball bounces back with less kinetic energy and cannot reach quite the same height. A well-inflated ball bounces better because it has more air inside. This allows it to push back faster, reducing the contact time and contact area in a collision and thus reducing the heat produced.

Why do stacked balls bounce higher?

When a golf ball collides with a basketball, the golf ball recoils at high speed in part because of the big difference in mass between the two balls. When a light object meets a heavy object, the heavy object hardly changes velocity. The light object recoils much quicker.

How many times can u bounce a ball?

As long as you don’t touch it on the way down and have control and ONE hand touching down on the ball on the way back up, your dribble is still good – and the ball can bounce infinite times (if time allows) in between.

How to calculate the bouncing ball geometric sequence?

To the top of the first bounce the ball travels down 4 a and back up 3 a. The remainder of the track of the ball is exactly as if it had fallen off a table of height 3 a – and simply by scaling we see that this would be 3 4 d. So we have 7 a + 3 4 d = d and it is easy to solve from there.

How many times does a bouncing ball bounce?

After the ball is dropped the initial 3 m, it bounces up and down a distance of 2.4 m. Each bounce after the first bounce, the ball travels 0.8 times the previous height twice — once upwards and once downwards. So, the total vertical distance is given by

How tall is a building when a ball bounces?

(Physical Science) Maddy drops a ball off of a building that is 60 feet high. Each time the ball bounces, it bounces back to ⅔ its previous height. If the ball continues to follow this pattern what will be the total distance that the ball travels?