Respuesta :
Given that the Ship traveling at 18 mph is 5 miles south of San Francisco, the rate of change of the distance from San Francisco is approximately 17.57 mph
How can the rate of change of the distance be found?
Given;
- Vertical distance from the path of the ship to San Francisco = 5 miles
- Rate at which the ship is traveling = 18 mph
Required;
The rate at which the distance from the ship to San Francisco is changing 1 hour after leaving the port.
Solution;
Let x represent the horizontal distance from the ship to San Francisco, and let y represent the vertical distance, we have;
Using Pythagorean theorem, we have;
The distance from the ship to San Francisco, d is; d² = x² + 4²
Which gives;
[tex]2\cdot d\cdot \dfrac{dd}{dt} = 2\cdot x \cdot \dfrac{dx}{dt} [/tex]
After 1 hour, we have;
x = 18 miles
Which gives;
d² = 18² + 4² = 340
d = 2•√(85)
[tex] \dfrac{dd}{dt} = \dfrac{2\cdot x \cdot \dfrac{dx}{dt}}{2\cdot d} [/tex]
Therefore;
[tex] \dfrac{dd}{dt} = \dfrac{36 \times 18}{2\times 2•√(85)} ≈ 17.57 [/tex]
The rate at which the distance between San Francisco is changing after 1 hour is, d ≈ 17.57 m/s
Learn more about Pythagorean theorem here:
https://brainly.com/question/12627912
