Question
Two ships leave a port at the same
time one travels due west at
and other due south at
Calculate how far apart the two ships
are ofter 4 hrs
time one travels due west at
and other due south at
Calculate how far apart the two ships
are ofter 4 hrs
Ask by Wang Bond. in Kenya
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After 4 hours, the two ships are approximately 132.68 km apart.
Solution
To calculate how far apart the two ships are after 4 hours, we need to find the distance each ship has traveled in that time.
Given:
- Ship 1 travels due west at
- Ship 2 travels due south at
- Time = 4 hours
-
Calculate the distance each ship has traveled in 4 hours:
- Distance = Speed * Time
For Ship 1 (west):- Distance =
For Ship 2 (south):- Distance =
-
Calculate the total distance between the two ships after 4 hours:
- The total distance between the two ships is the hypotenuse of a right-angled triangle formed by the distances traveled by each ship.
We can use the Pythagorean theorem to find the total distance:
Let’s calculate the distances and the total distance between the two ships after 4 hours.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Multiply the numbers:
Calculate or simplify the expression.
Calculate the value by following steps: - step0: Calculate:
- step1: Multiply the numbers:
Calculate or simplify the expression.
Calculate the value by following steps: - step0: Calculate:
- step1: Convert the expressions:
- step2: Convert the expressions:
- step3: Transform the expression:
- step4: Use the properties of radicals:
- step5: Simplify the expression:
After 4 hours, the two ships are approximately 132.68 km apart.
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Simplify this solution Bonus Knowledge
To find out how far apart the two ships are after 4 hours, we first need to calculate the distance traveled by each ship in that time.
For the westbound ship:
Distance = Speed × Time =
Distance = Speed × Time =
For the southbound ship:
Distance = Speed × Time =
Distance = Speed × Time =
Now, we can treat the positions of the two ships as the two sides of a right triangle, where the distance between the two ships is the hypotenuse. Using the Pythagorean theorem:
Distance apart =
So, after 4 hours, the two ships are approximately 132.6 km apart.
