Let's first draw a picture of the situation given by the problem. The ball will first fall 14m, then bounce up (14 * 5/6) m and fall back with the same distance, then bounce up (14 * 5/6 * 5/6) m and fall back with the same distance, so on and so forth.
Hence, we can set an expression for the total distance travelled:
Distance = 14 + 2 * (geometric series).
Now, let's find the geometric series. It is quite easy to find that the multiplying ratio of the sequence is 5/6 because that's the factor the height is changing by. Furthermore, the first term in the sequence would be 14 * 5/6 as we kind of separated 14 out of the series. Hence, the first term would be 35 / 3.
You may know that the equation to solve for a geometric series is (first term) / (1 - r). We can use this equation to solve for geometric series.
S = (35/3) / ( 1 - (5/6) ) = 70.
Now, back to the original expression:
Distance = 14 + 2 * 70 = 154.
Therefore, the total distance the ball will travel is 154 m.
Hi,
Thank you for your question.
Let's first draw a picture of the situation given by the problem. The ball will first fall 14m, then bounce up (14 * 5/6) m and fall back with the same distance, then bounce up (14 * 5/6 * 5/6) m and fall back with the same distance, so on and so forth.
Hence, we can set an expression for the total distance travelled:
Distance = 14 + 2 * (geometric series).
Now, let's find the geometric series. It is quite easy to find that the multiplying ratio of the sequence is 5/6 because that's the factor the height is changing by. Furthermore, the first term in the sequence would be 14 * 5/6 as we kind of separated 14 out of the series. Hence, the first term would be 35 / 3.
You may know that the equation to solve for a geometric series is (first term) / (1 - r). We can use this equation to solve for geometric series.
S = (35/3) / ( 1 - (5/6) ) = 70.
Now, back to the original expression:
Distance = 14 + 2 * 70 = 154.
Therefore, the total distance the ball will travel is 154 m.
Does this answer your question?