Two row boats start at the same location, and start traveling apart along straight lines which meet at an angle of π3. Boat A is traveling at a rate of 5 miles per hour directly east, and boat B is traveling at a rate of 10 miles per hour going both north and east. How fast is the distance between the rowboats increasing 3 hours into the journey?

Question

Mathematics

Elsie Mccann

2 September, 07:41

Two row boats start at the same location, and start traveling apart along straight lines which meet at an angle of π3. Boat A is traveling at a rate of 5 miles per hour directly east, and boat B is traveling at a rate of 10 miles per hour going both north and east. How fast is the distance between the rowboats increasing 3 hours into the journey?

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Answers (1)

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Salma Soto · Answer 1

5√3 miles per hour

Step-by-step explanation:

Throughout their journey, the component of velocity of rowboat B to the east is the same as that of rowboat A:

(10 mph) (cos (π/3)) = 5 mph

Meanwhile, the component of velocity of rowboat B to the north is ...

(10 mph) (sin (π/3)) = 5√3 mph

Since rowboat A is always traveling in a direction that is at right angles to the direction between the boats, it contributes nothing to their relative speed. Since rowboat B is always directly north of rowboat A, its speed to the north is their relative speed.

The distance between the rowboats is increasing at 5√3 mph ≈ 8.66 mph.