Question

Can someone please explain how to solve number sixteen using those two equations?

Answer 1

`v=14m^(2)/s`

Step-by-step explanation:

First, let's write out what we already know

• K= ΔU
• K = 1/2 mv²
• ΔU = mgh
• g = 9.8 m/s²
• h = 10m
• Therefore: 1/2 mv² = (m)(9.8m/s²)(10m)

Combine like terms and then solve accordingly.

1/2 mv²= (10m²)(9.8m/s²)

1/2 mv²= 98m³/s²

v²= 2m(98m³/s²)

v² = 196m⁴/s²

`\sqrt{v^(2) }` =
`\sqrt{(196m^(4) )/(s^(2) )`

v = 14m²/s

Answer 2

Hello!

First, we know K = ΔUg. (From now on, I'm going to use a lowercase g as your subscript g). We therefore can say that 1/2mv^2 = mgh, as K = 1/2mv^2, ΔUg = mgh, and K and ΔUg are equal.

From this equation, substitute in values and divide both sides by m.

1/2mv^2 = mgh

1/2mv^2 = m(9.8)(10)

(1/2mv^2) / m = (m(9.8)(10)) / m

1/2v^2 = (9.8)(10)

Now, we have an easily solvable equation.

1/2v^2 = (9.8)(10)

1/2v^2 = 98

v^2 = 196

v = 14

Therefore, your answer is v = 14.

Hope this helps!