Question

A high fountain of water is in the centre of a circular pool of water. You walk the circumference of the pool and measure it to be 1.50 × 10^2 meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is 55.0°. How high is the fountain?

Answer 1

Answer on Question #72714, Physics / Mechanics | Relativity |

A high fountain of water is in the centre of a circular pool of water. You walk the circumference of the pool and measure it to be $1.50 \times 10^{2}$ meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is $55.0{}^{\circ}$. How high is the fountain?

Solution:

From the circumference we can find the radius of the pool $R = \frac{L}{2\pi} = \frac{150m}{2\pi} = 23.9m$.

The height of the fontain is $H = R \tan(55{}^{\circ}) = 23.9 \, \text{m} \cdot 1.428 = 34.1 \, \text{m}$.

Answer: $H = 34.1 \, \text{m}$.

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