Answer:
Da=(1/4)Db
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²
When s = Da, t = t
When s = Db, t = 2t
Dividing the two equations
Hence, Da=(1/4)Db
Answer:
U = 1 / r²
Explanation:
In this exercise they do not ask for potential energy giving the expression of force, since these two quantities are related
F = - dU / dr
this derivative is a gradient, that is, a directional derivative, so we must have
dU = - F. dr
the esxresion for strength is
F = B / r³
let's replace
∫ dU = - ∫ B / r³ dr
in this case the force and the displacement are parallel, therefore the scalar product is reduced to the algebraic product
let's evaluate the integrals
U - Uo = -B (- / 2r² + 1 / 2r₀²)
To complete the calculation we must fix the energy at a point, in general the most common choice is to make the potential energy zero (Uo = 0) for when the distance is infinite (r = ∞)
U = B / 2r²
we substitute the value of B = 2
U = 1 / r²
Answer:
We know that the speed of sound is 343 m/s in air
we are also given the distance of the boat from the shore
From the provided data, we can easily find the time taken by the sound to reach the shore using the second equation of motion
s = ut + 1/2 at²
since the acceleration of sound is 0:
s = ut + 1/2 (0)t²
s = ut <em>(here, u is the speed of sound , s is the distance travelled and t is the time taken)</em>
Replacing the variables in the equation with the values we know
1200 = 343 * t
t = 1200 / 343
t = 3.5 seconds (approx)
Therefore, the sound of the gun will be heard at the shore, 3.5 seconds after being fired
Answer:
This is because below 4°c, water unlike other materials becomes less dense when it's temperature is further lowered.
Explanation:
Due to the unusual nature of water; at about 4°c, the behavior of the density of water in relation to its temperature reverses. This means that water becomes less dense as it becomes colder below 4°c. The colder parts therefore floats to the top of the water body while the warmer part sinks allowing the top to freeze and the remaining body below to remain in its liquid state.
The freezing of the top of the lake alone protects the remaining depth of water from freezing by acting as an insulator and preventing further heat loss from the water to the ambient space. If this had not been the case, and water froze all through, marine lives will freeze to death and it will be more difficult to melt the ice come the next summer.
This behavior is due to the hydrogen bonding of the water molecules.
