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Mary threw a ball onto level ground from a height of 2 m - Leaving Cert Mathematics - Question 1 - 2015
Question 1
Mary threw a ball onto level ground from a height of 2 m. Each time the ball hit the ground it bounced back up to \(\frac{3}{4}\) of the height of the previous bounc... show full transcript
Worked Solution & Example Answer:Mary threw a ball onto level ground from a height of 2 m - Leaving Cert Mathematics - Question 1 - 2015
Step 1
Step 2
Find, in metres, the total vertical distance (up and down) the ball had travelled when it hit the ground for the 5th time. Give your answer in fraction form.
Answer
The total distance travelled can be calculated by adding the height of each bounce and the distance fallen:
[2 + 2 \left(\frac{3}{2} + \frac{9}{8} + \frac{27}{32} + \frac{81}{128}\right) = 2 + 2 \cdot \frac{525}{128} = 2 + \frac{653}{64} = 10 \frac{13}{64} \text{ m}]
Step 3
If the ball were to continue to bounce indefinitely, find, in metres, the total vertical distance it would travel.
Answer
The total distance travelled can be expressed as:
[2 + 2 \left(\frac{3}{2} + \frac{9}{8} + \frac{27}{32} + \ldots\right) = 2 + 2 \cdot \frac{\frac{3}{2}}{1 - \frac{1}{4}} = 2 + 2 \cdot \frac{\frac{3}{2}}{\frac{3}{4}} = 2 + 2 \cdot 2 = 14 \text{ m}]