The crossbar of a goal post on a professional American football field sits at a height of 3.05 meters (10 feet) above the field.

The equations are h = v₀² / 2g, and h = k/4g x².

The wavelength can be calculated as Planck's constant divided by the momentum of the ball.
This translates to:
lambda = h / p.............> equation I
Momentum is equal to mass times velocity............> equation II

By substituting equation II into equation I, we obtain:
lambda = h / mv
Here are the values provided:
lambda = 8.92 * 10^-34 m
Planck's constant = 6.625 * 10^-34
velocity = 40 m/sec

Substituting these values into the previous equation, we calculate the mass as follows:
8.92*10^-34 = (6.625*10^-34) / (40*m)
mass = 0.0185678 kg

Red ants rely on plants since they inhabit some of them and they consume sweet substances, such as sugar that comes from sugarcane, while squirrels depend on plants for nuts that they eat.

Answer:

The water level increases more when the cube is above the raft before it sinks.

Explanation:

The principle involved is based on Archimedes' theory, which states that immersing an object in water will raise the initial water level. This means that the height of the water in the container increases. The increase in water volume corresponds to the volume of the submerged object.

We can consider two scenarios: when the steel cube rests on the raft and when it settles at the pool's bottom.

When the cube rests at the pool’s bottom, the volume will indeed rise, and we can ascertain this using the cube's volume.

Vc = 0.45*0.45*0.45 = 0.0911 [m^3]

When an object floats, it's because the densities of the object and water are in equilibrium.

The formula for density is:

Ro = m/V

where:

m= mass [kg]

V = volume [m^3]

The buoyant force can be calculated with this equation:

Vs > Vc indicates that the combined volume of the raft and the cube exceeds that of the cube alone resting at the bottom of the pool. Hence, when the cube is positioned above the raft, the water level rises more before it becomes submerged.

1) The initial velocity is zero. 2) We consider the downward direction as positive.
3) h = 25.66 m.
Explanation:
This is a problem of free fall.
1) In free fall, the initial velocity starts at zero, and acceleration remains constant throughout, equal to gravity.
2) It's common to choose downward as the positive direction.
3) For the latter part of the fall:
y₀ - y = h/2 when t = 1 s,
y = y₀ + v₁ t + ½ g t²,
with v₁ being the initial velocity at height h / 2,
v₁ t = (y - y₀) - ½ g t².
v₁ = h / 2 - ½ g t².
Now, let's set up the first interval equation:
v₁² = v₀² + 2 g (y₁ - y₀).
Since in this case v₀ = 0,
v₁² = 2 g (y₁ - y₀) = 2g h/2.
Next, our equations become:
v₁² = (h/2 - g/2)² and v₁² = (2g h / 2).
Thus, solving the quadratic equation leads to:
h² - 3 g h + g² = 0, which simplifies to h² - 29.4 h + 96.04 = 0.
Finally, solving this yields h = 25.66 m as the height.