Solve Applied Problems Involving Vectors
-A power boat in still water maintains a speed of 45 miles per hour. The boat heads directly across a river perpendicular to the current which has a speed of 8 miles per hour. Find the actual speed and direction of the boat.
A) 46 miles per hour; $10 ^ { \circ }$ off course
B) 45 miles per hour; $10 ^ { \circ }$ off course
C) 22 miles per hour; $21 ^ { \circ }$ off course
D) 17 miles per hour; $28 ^ { \circ }$ off course

Question

Quizplus · Accepted Answer

The actual speed of the boat is found by calculating the magnitude of the resultant vector, which is the hypotenuse of a right triangle with sides 45 mph (boat's speed in still water) and 8 mph (current's speed). Using the Pythagorean theorem, the actual speed is $\sqrt{45^2 + 8^2} = \sqrt{2025 + 64} = \sqrt{2089} \approx 46$ mph. The direction off course, $\theta$, can be found using the tangent function: $\tan(\theta) = \frac{8}{45}$, which gives $\theta \approx 10^\circ$.

Solve Applied Problems Involving Vectors -A Power Boat in Still 10∘10 ^ { \circ }10∘

Solve Applied Problems Involving Vectors
-A Power Boat in Still $10 ^ { \circ }$