A cannon can make a maximum angle of 30 degrees with the horizon. What is the minimum speed of a cannon ball if it must clear a
1 answer:
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Answer:
19.5°
Explanation:
The energy of the mass must be conserved. The energy is given by:
1)
where m is the mass, v is the velocity and h is the hight of the mass.
Let the height at the lowest point of the be h=0, the energy of the mass will be:
2)
The energy when the mass comes to a stop will be:
3)
Setting equations 2 and 3 equal and solving for height h will give:
4)
The angle ∅ of the string with the vertical with the mass at the highest point will be given by:
5)
where l is the lenght of the string.
Combining equations 4 and 5 and solving for ∅:
6)
Answer:
The volume of the final solution, V = 0.0305L
Explanation:
Number of moles = Concentration * volume
Concentration of HA = 1.00 * 10⁻⁴M
Volume of HA = 1000mL = 1 L
Number of moles of HA = 1.00 * 10⁻⁴ * 1
Number of moles of HA = 1.00 * 10⁻⁴ mols
Equation of reaction:
HA → H⁺ + A⁻
If 1 mol of HA produces 1 mol of H⁺ and A⁻, 1.00 * 10⁻⁴ mol of HA will produce 1.00 * 10⁻⁴ mol of H⁺ and A⁻.
Since only 16% dissociation occurs = 0.16
Number of moles of H⁺ produced = 0.16 * 1.00 * 10⁻⁴
Number of moles of H⁺ produced = 1.6 * 10⁻⁵mols
Number of moles of A⁻ produced = 0.16 * 1.00 * 10⁻⁴
Number of moles of A⁻ produced = 1.6 * 10⁻⁵mols
Since 16% of HA dissociated into H⁺ and A⁻, 84% of HA is left
Number of mols of HA left = 0.84 * 1.00 * 10⁻⁴
Number of mols of HA left = 8.4 * 10⁻⁵mols
Concentration = num of moles/volume
Let the volume of the final solution be V
Conc of HA = 8.4 * 10⁻⁵/V
Conc of H⁺ = 1.6 * 10⁻⁵/V
Conc of A⁻ = 1.6 * 10⁻⁵/V
To calculate the dissociation constant