Question
A motor boat due east at 10m/s on a current moving towards S 30 degree W @ 5.0m/s. Find the resultant value of the boat and the direction.
Answers
drwls
The velocity of the boat with respect to land equals the VECTOR sum of the water velocity and the boat's speed with relative to the water.
If i and j are unit vectors East and north,
V(with respect to land) =
10 i + -5 sin30 i - 5 cos30 j
= 7.5 i - 4.33 j
Speed = sqrt[(7.5)^2 + (4.33)^2]
= 8.66 m/s
The direction is arctan(4.33/7.5)= 30 degrees South of East
If i and j are unit vectors East and north,
V(with respect to land) =
10 i + -5 sin30 i - 5 cos30 j
= 7.5 i - 4.33 j
Speed = sqrt[(7.5)^2 + (4.33)^2]
= 8.66 m/s
The direction is arctan(4.33/7.5)= 30 degrees South of East