To calculate the height of the tower from which the arrow is projected, we will use the vertical motion equations under the influence of gravity.
The time it takes for the arrow to reach the ground is given as \( t = 7 \) seconds. The height from which the arrow is projected can be calculated using the formula for the distance fallen under gravity, which is:
\[ h = \frac{1}{2} g t^2 \]
Where:
- \( h \) is the height of the tower,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( t \) is the time in seconds.
Plugging in the values:
\[ h = \frac{1}{2} \cdot 9.81 , \text{m/s}^2 \cdot (7 , \text{s})^2 \]
Now, calculate it step by step:
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Calculate \( (7 , \text{s})^2 \): \[ (7)^2 = 49 , \text{s}^2 \]
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Multiply by \( g \): \[ 9.81 , \text{m/s}^2 \cdot 49 , \text{s}^2 = 481.69 , \text{m} \]
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Now, apply the factor of \( \frac{1}{2} \): \[ h = \frac{1}{2} \cdot 481.69 \approx 240.845 , \text{m} \]
Therefore, the height of the tower is approximately 240.85 meters.
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