Question

A fishing boat is traveling 25 miles per hour in the direction on S 65 W. If it hits a current traveling at 6 miles per hour in the N 15 W direction. Find the resultant magnitude and direction of the boat.

Answer 1

Let's draw the scenario:

To be able to get the resultant magnitude, let's add the x and y components of the current and the boat.

Step 1: Let's break down the x and y components of the direction of the boat.

Boat: 25 miles/hr. S 65 W

x-component = 25sin(65°) = 22.66 West = -22.66 to represent that it is in the West Direction.

y-component = 25cos(65°) = 10.57 South = -10.57 to represent that it's in Downward Direction.

Current: 6 miles/hour N 15 W

x-component = 6sin(15°) = 1.55 West = -1.55 to represent that it is in the West Direction.

y-component = 6cos(15°) = 5.80 North = 5.80 to represent that it's in Upwad Direction.

Let's now add each x and y component.

Resultant x-component = -22.66 + -1.55 = -24.21 = 24.21 miles/hr. West

Resultant y-component = 5.80 - 22.66 = -16.86 = 16.86 miles/hr. South

Therefore the Resultant is equal to:

`\text{ R = }\sqrt[]{24.21^2+16.86^2}`
`R\text{ = 24.21 miles/hour}`

Let's determine the angle at S-W:

`\theta=\tan ^(-1)((16.86)/(24.21))`
`\theta=34.85^(\circ)`

Therefore, the resultant magnitude and direction of the boat is,

`24.21\text{ miles/hour at S 34.85 W}`