The altitude of a hang glider is increasing at a rate of 6.80 m/s. At the same time, the shadow of the glider moves along the ground at a speed of 15.5 m/s when the Sun is directly overhead. Find the magnitude of the glider's velocity.

Options

A. 4.72 m/s
B. 14.1 m/s
C. 9.44 m/s
D. 16.9 m/s

Answer

To find the magnitude of the glider's velocity, we can use the Pythagorean theorem since the glider's altitude (vertical component) and the speed of its shadow (horizontal component) are perpendicular to each other.

### Step-by-Step Solution:

1. **Identify the components of velocity**:
- The vertical component of the glider's velocity (altitude increase) is given as \( v_y = 6.80 \, \text{m/s} \).
- The horizontal component of the glider's velocity (shadow movement) is given as \( v_x = 15.5 \, \text{m/s} \).

2. **Use the Pythagorean theorem**:
The magnitude of the resultant velocity \( v \) can be calculated using the formula:
\[ v = \sqrt{v_x^2 + v_y^2} \]

3. **Substitute the values**:
\[ v = \sqrt{(15.5)^2 + (6.8)^2} \]

4. **Calculate the squares**:
- \( (15.5)^2 = 240.25 \)
- \( (6.8)^2 = 46.24 \)

5. **Add the squares**:
\[ v = \sqrt{240.25 + 46.24} = \sqrt{286.49} \]

6. **Calculate the square root**:
\[ v \approx 16.92 \, \text{m/s} \]

### Final Answer:
The magnitude of the glider's velocity is approximately \( 16.92 \, \text{m/s} \).

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