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At a lab investigating fire extinguisher foams, a heavy ball is accidentally dropped into a deep vat of foam from a crane 6.10 m above the foam. After entering the foam, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the foam. The ball reaches the bottom 3.20 s after it is released. How deep is the vat?

Respuesta :

boffeemadrid

Answer:

22.8077659955 m deep

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 6.1+0^2}\\\Rightarrow v=10.9399268736\ m/s[/tex]

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{10.9399268736-0}{9.81}\\\Rightarrow t=1.11518112881\ s[/tex]

Time taken to fall through the foam

[tex]3.2-1.11518112881=2.08481887119\ s[/tex]

Distance is given by

[tex]s=vt\\\Rightarrow s=10.9399268736\times 2.08481887119\\\Rightarrow s=22.8077659955\ m[/tex]

The vat is 22.8077659955 m deep

Eduard22sly

The depth of the vat obtained is 44.076 m

Data obtained from the question

  • Height of crane above the vat = 6.10 m
  • Time to reach the bottom of the vat from the crane = 3.20 s
  • Depth of vat =?

Determination of the height from the crane to the bottom of the vat

  • Time to reach the bottom of the vat from the crane (t) = 3.20 s
  • Acceleration due to gravity (g) =?
  • Height from crane to bottom of vat (H) =?

H = ½gt²

H = ½ × 9.8 × 3.2²

H = 4.9 × 10.24

H = 50.176 m

How to determine the depth of the vat

  • Height from crane to bottom of vat (H) = 50.176 m
  • Height of crane above the vat (h) = 6.10 m
  • Depth of vat =?

Depth of vat = H – h

Depth of vat = 50.176 – 6.10

Depth of vat = 44.076 m

Learn more about motion under gravity:

https://brainly.com/question/20385439

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