When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity?

5.1^2 + v^2 = 7.0^2

Well, it sounds like Jeff is quite the speedy runner! As for the vertical component of his velocity, let's see if we can figure that out.

We know that Jeff's total velocity is 7.0 m/s and the horizontal component is 5.1 m/s. So, if we imagine Jeff running up a hill, the vertical component of his velocity will be the remaining component.

To do a little math magic, we can use the Pythagorean theorem. Let's call the vertical component "Vv":

Vv² + 5.1² = 7.0²

Now, let's solve for Vv. But before we do, let me ask you something: What do you call a math teacher who's having a sleepless night?
A wide awake-er! 😄

Now that we've had a quick laugh, let's continue.

Vv² + 26.01 = 49

Subtracting 26.01 from both sides:

Vv² = 22.99

And taking the square root of both sides:

Vv ≈ 4.796

Therefore, the vertical component of Jeff's velocity is approximately 4.796 m/s.

I hope this helps, and remember that even in math, laughter is the best medicine!

To find the vertical component of Jeff's velocity, you can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the diagonal side of a right triangle) is equal to the sum of the squares of the other two sides.

In this case, the horizontal component of Jeff's velocity (or the adjacent side) is 5.1 m/s, and the total velocity (or the hypotenuse) is 7.0 m/s. Let's denote the vertical component as 'v'.

Using the Pythagorean theorem:

7.0^2 = 5.1^2 + v^2

49 = 26.01 + v^2

v^2 = 49 - 26.01

v^2 = 22.99

Taking the square root of both sides:

v = sqrt(22.99)

v ≈ 4.793 m/s

Therefore, the vertical component of Jeff's velocity is approximately 4.793 m/s.

To find the vertical component of Jeff's velocity, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, Jeff's velocity forms a right triangle, where the horizontal component is one side, the vertical component is another side, and the hypotenuse is his actual velocity. We are given the value of the horizontal component (5.1 m/s) and the overall velocity (7.0 m/s). Let's call the vertical component v.

Using the Pythagorean theorem, we can write the equation:

(5.1 m/s)^2 + v^2 = (7.0 m/s)^2

Simplifying the equation:

26.01 m^2/s^2 + v^2 = 49.00 m^2/s^2

We can now solve for v by isolating it on one side of the equation:

v^2 = 49.00 m^2/s^2 - 26.01 m^2/s^2

v^2 = 22.99 m^2/s^2

To solve for v, we take the square root of both sides:

v = √(22.99 m^2/s^2)

Using a calculator, we can find:

v ≈ 4.79 m/s

Therefore, the vertical component of Jeff's velocity is approximately 4.79 m/s.