Use the Pythagorean theorem to answer this question. Becca paddles a boat from the south bank of a stream to the north bank. She paddles at a rate of 8 mph. The stream is flowing west at a rate of 6 mph. What is Becca's actual velocity?
Answers
This is a question on perpendicular vectors.
The vector in question is velocity.
The velocity to the North is perpendicular to the velocity to the West.
For perpendicular vectors, the resultant vector is usually the hypotenuse of the right angled formed.
Now our base = 6
Height = 8
By pythagorean theorem:
Let h be the hypotenuse then :
h² = 6² + 8²
h² = 100
h = 10
= 10 m/s
She is going north at 8, she is going west at 6, vector north 8 units long.
The ending of the vector west (left) 6 units long.
Of course, the two vectors by drawing the hypotenuse from lower right to upper left and if your are find the length of that hypotenuse.
In addition, we done magnitude of your resultant velocity.
Base is the angle west of north of the resultant vector. Its tangent is 6/8 or ¾.