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A tree grows at a rate of 0.5 m/yr . Wh...

A tree grows at a rate of 0.5 m/yr . What will be the height of a board fixed at 1.5 m above the base, five years ago

A

4 m

B

3.5 m

C

1.5 m

D

4.5 m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the height of a board that was fixed at 1.5 meters above the base of a tree, considering the tree's growth over the past five years. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Growth Rate The tree grows at a rate of 0.5 meters per year. ### Step 2: Calculate Total Growth Over Five Years To find out how much the tree has grown in five years, we multiply the growth rate by the number of years: \[ \text{Total Growth} = \text{Growth Rate} \times \text{Number of Years} = 0.5 \, \text{m/year} \times 5 \, \text{years} = 2.5 \, \text{meters} \] ### Step 3: Determine the Height of the Tree Five Years Ago If the tree has grown 2.5 meters over the last five years, we need to find out how tall the tree was five years ago. To do this, we subtract the total growth from the current height of the tree: \[ \text{Height of Tree Five Years Ago} = \text{Current Height} - \text{Total Growth} \] Since the board is fixed at 1.5 meters above the base, we can assume that the height of the tree at that time was equal to the height of the board plus the growth: \[ \text{Height of Tree Five Years Ago} = 1.5 \, \text{meters} - 2.5 \, \text{meters} = -1.0 \, \text{meters} \] This indicates that the tree was not tall enough to reach the board five years ago. ### Step 4: Find the Height of the Board Relative to the Tree's Growth Since the board is fixed at 1.5 meters above the base, and the tree has grown to a height of 2.5 meters after five years, we can find the new position of the board relative to the tree: \[ \text{New Height of the Board} = \text{Height of the Board} + \text{Total Growth} = 1.5 \, \text{meters} + 2.5 \, \text{meters} = 4.0 \, \text{meters} \] ### Step 5: Conclusion The height of the board fixed at 1.5 meters above the base remains at 1.5 meters above the base of the tree, regardless of the tree's growth. Therefore, the height of the board five years ago would still be 1.5 meters above the base. ### Final Answer The height of the board fixed at 1.5 meters above the base, five years ago, is still **1.5 meters**. ---
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