A stone is thrown horizontally at 15 m/s from the top of a cliff 44 meters high. How far from the base does the stone hit the ground?

  44.9 m

Explanation:

For ballistic motion in x-y coordinates, an appropriate equation can be ...

  y(x) = -4.9(x·sec(α)/v)² +tan(α)x + h0

where α is the angle of launch from the horizontal, and v is the magnitude of the launch velocity.

Here, we have v = 15 m/s, and α = 0, so the equation reduces to ...

  y = -4.9/225x^2 +44

For y = 0, we can find x to be ...

  x^2 = (44×225/4.9) ≈ 2020.41

  x ≈ 44.949

The stone hits the ground about 44.9 meters from the base of the cliff.

The question is incomplete, here is the complete question:

Calculate the pH of a solution prepared by dissolving 0.370 mol of formic acid (HCO₂H) and 0.230 mol of sodium formate (NaCO₂H) in water sufficient to yield 1.00 L of solution. The Ka of formic acid is 1.77 × 10⁻⁴

a) 2.099

b) 10.463

c) 3.546

d) 2.307

e) 3.952

The pH of the solution is 3.546

Explanation:

We are given:

Moles of formic acid = 0.370 moles

Moles of sodium formate = 0.230 moles

Volume of solution = 1 L

To calculate the molarity of solution, we use the equation:

To calculate the pH of acidic buffer, we use the equation given by Henderson Hasselbalch:  

= negative logarithm of acid dissociation constant of formic acid = 3.75

pH = ?  

Putting values in above equation, we get:  

Hence, the pH of the solution is 3.546