Question 813578: A boat is traveling 12 mph on a compass bearing of 180 degrees. There is a current of four mph flowing from east to west. What is the actual speed and direction of the boat relative to dry land?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! use vector velocities:
b: magnitude = 12, direction = 180 degrees
w: magnitude = 4, direction = 270 degrees
---
we want the vector sum:
v = b + w
---
because the vectors are perpendicular, we can use the pythagorean theorem for the magnitude of v:
---
magnitude of v:
M(v) = sqrt( bb + ww )
M(v) = sqrt( 144 + 16 )
M(v) = 12.649111
---
direction of v:
for the direction of v we need the small angle (A) of the right triangle:
tan(A) = opp/adj = 4/12 = 1/3
A = arctan(1/3) = 18.434949 degrees
D(v) = 180 + 18.434949 = 198.434949 degrees
---
Answer:
from dry land the boat will appear to be moving on a bearing and speed of:
198.4 degrees at 12.7 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
|
|
|
