Question

Two ships left a port at the same time. One ship traveled at a speed of 19 miles per hour at a heading of 310°. The other ship traveled at a speed of 26 miles per hour at a heading of 195°. Find the distance between the two ships after 10 hours of travel. (Round your answer to the nearest mile.)

Answer 1

381 miles

Explanation:

After 10 hours, the first ship travels 190 miles. The second ship travels 260 miles.

Find the x and y components of each ship.

x₁ = 190 mi cos 310° = 122.13 mi

y₁ = 190 mi sin 310° = -145.55 mi

x₂ = 260 mi cos 195° = -251.14 mi

y₂ = 260 mi sin 195° = -67.29 mi

The difference in components is:

x = x₂ − x₁ = -373.27 mi

y = y₂ − y₁ = 78.26 mi

The magnitude is:

d² = x² + y²

d² = (-373.27 mi)² + (78.26 mi)²

d ≈ 381 mi