8. na₂o₂ + h₂(so₄) na(so₄) + h₂o₂

9. n₂ + h₂ nh₃

10. al +o₂ al₂o₃

11. kmno₄ k₂o + mno + o₂

Answers:

8. Na₂O₂ + H₂(SO₄) → Na₂(SO₄) + H₂O₂

9. N₂ + 3 H₂ → 2 NH₃

10. 4 Al + 3 O₂ → 2 Al₂O₃

11. 4 KMnO₄ → 2 K₂O + 4 MnO + 5 O₂

Step by step solution:

8. Na₂O₂ + H₂(SO₄) → Na₂(SO₄) + H₂O₂

In this chemical equation we have:

On the left side:          On the right side:

Na: 2 atoms                 Na: 2 atoms

O: 2+4=6 atoms           O: 4+2=6 atoms

H: 2 atoms                    H: 2 atoms

S: 1 atom                        S: 1 atom

We have the same quantity of atoms on both sides of the equation, then the equation is balanced.

9. N₂ + H₂ → NH₃

In this chemical equation we have:

On the left side:          On the right side:

Na: 2 atoms                 Na: 1 atom

H: 2 atoms                   H: 3 atoms

The equation is not balanced.

We need to multiply the molecule of NH₃ on the right side of the equation by 2 to get 2 Na atoms on the right side:

N₂ + H₂ → 2 NH₃

Now, we have 2(3)=6 H atoms on the right side of the equation, then we must multiply the molecule of H₂ on the left side by 3 to get 3(2)=6 H atoms on the left side of the equation:

N₂ + 3 H₂ → 2 NH₃

10. Al + O₂ → Al₂O₃

In this chemical equation we have:

On the left side:          On the right side:

Al: 1 atom                     Al: 2 atoms

O: 2 atoms                   O: 3 atoms

The equation is not balanced.

The least common multiple between the quantity of atoms of O of the left side (2) and the right side (3) is 2*3=6, then let's multiply the molecule of O₂ on the left side by 3 and the molecule of  Al₂O₃ on the right side by 2 to get 6 O atoms on both side of the equation:

Al + 3 O₂ → 2 Al₂O₃

Now we have 2(2)=4 Al atoms on the right side of the equation and only 1 Al atom on the left side, then let's multiply the Al atom on the left side by 4:

4 Al + 3 O₂ → 2 Al₂O₃

11. KMnO₄ → K₂O + MnO + O₂

In this chemical equation we have:

On the left side:          On the right side:

K: 1 atom                      K: 2 atoms

Mn: 1 atom                   Mn: 1 atom

O: 4 atoms                   O: 1+1+2=4 atoms

The equation is not balanced

If we suppose that the coefficients are:

a KMnO₄ → b K₂O + c MnO + d O₂

We have on the left side "a" Mn atoms and on the right side "c" Mn atoms, and they must be equal then a=c:

a KMnO₄ → b K₂O + a MnO + d O₂

We have "a" K atoms on the left side and b(2)=2b K atoms on the right side, then a=2b

And we have on the left side a(4)=4a O atoms and on the right side

b+a+d(2)=b+a+2d O atoms, and they must be equal, then:

4a=b+a+2d

and a=2b, replacing in the equation above:

4(2b)=b+2b+2d

8b=b+2b+2d

Adding like terms on the left side of the equation:

8b=3b+2d

Solving for d: Subtracting 3b from both sides of the equation:

8b-3b=3b+2d-3b

5b=2d

Dividing both sides of the equation by 2:

5b/2=2d/2

5b/2=d

d=5b/2

Then b must be an even number to get a whole number for d, using the least even number for b=2

d=5(2)/2→d=5

and a=2b=2(2)→a=4

Then the equation balanced is:

4 KMnO₄ → 2 K₂O + 4 MnO + 5 O₂

Now we have:

On the left side:          On the right side:

K: 4 atoms                   K: 2(2)=4 atoms

Mn: 4 atoms                Mn: 4 atoms

O: 4(4)=16 atoms         O: 2+4+5(2)=2+4+10=16 atoms

The equation is balanced

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft