use the phythagorean theroem 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 beccá actual velocity. I need to understand how to figure this quesiton out.
she is going north at 8
she is going west at 6
Draw a vector north (up) 8 units long.
At the tip of that, the north end, draw a vector west(left) 6 units long.
Add those two vectors by drawing the hypotenuse from lower right to upper left.
Find the length of that hypotenuse.
That is the magnitude of your resultant velocity.
The angle the hypotenuse makes with the north vector at its base is the angle west of north of the resultant vector. Its tangent is 6/8 or 3/4
Rate of 8 mph and rate of 6 mph what is the velocity?
To answer this question using the Pythagorean theorem, we need to consider the velocities in different directions. Let's break down the motion of Becca's boat into two components: the velocity due to her paddling, and the velocity of the stream.
The velocity directly due to Becca's paddling is 8 mph. However, because the stream is flowing west at a rate of 6 mph, it affects Becca's overall velocity.
Using the Pythagorean theorem, we can determine Becca's actual velocity (v) by considering the horizontal and vertical components of her velocity:
v^2 = (8 mph)^2 + (6 mph)^2
v^2 = 64 mph^2 + 36 mph^2
v^2 = 100 mph^2
To find v, we take the square root of both sides:
v = √(100 mph^2)
v = 10 mph
Therefore, Becca's actual velocity is 10 mph.
To solve this question using the Pythagorean Theorem, we need to understand that velocity is a vector quantity, which means it has both magnitude (speed) and direction.
In this case, Becca's boat is moving in two different directions simultaneously. She is moving north across the stream, and the current of the stream is pushing her westward. To find Becca's actual velocity, we need to combine both the effects of her paddling speed and the current.
Let's break down the problem into components:
1. The northward velocity component: Becca's speed is given as 8 mph, which represents her northward velocity. Since she is moving directly against the current, the stream's westward velocity component doesn't affect this part. Therefore, Becca's northward velocity is 8 mph.
2. The westward velocity component: The stream's velocity is given as 6 mph westward. This velocity acts perpendicular to Becca's northward velocity. To combine these velocities, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (the resulting velocity) is equal to the sum of the squares of the other two sides (the northward and westward velocities).
Let's use the formula to find Becca's resulting velocity:
(Resultant velocity)^2 = (Northward velocity)^2 + (Westward velocity)^2
(Resultant velocity)^2 = (8 mph)^2 + (6 mph)^2
(Resultant velocity)^2 = 64 + 36
(Resultant velocity)^2 = 100
Resultant velocity = √100
Resultant velocity = 10 mph
Therefore, Becca's actual velocity (resultant velocity) is 10 mph.