Answer:
68.8 Hz
137.6 Hz, 206.4 Hz
Explanation:
L = Length of tube = 2.5 m
v = Velocity of sound in air = 344 m/s
Distance between nodes is given by
Where n = 0, 1, 2, 3, ...
Making n+1 = n
where n = 1, 2, 3 .....
For fundamental frequency n = 1
Frequency is given by
The fundamental frequency is 68.8 Hz
First overtone
Second overtone
The overtones are 137.6 Hz, 206.4 Hz
1) Time in the air: 0.78 s
The motion of the ball is a projectile motion, which consists of two independent motions:
- A horizontal motion with constant horizontal velocity
- A vertical motion with constant downward acceleration of
(acceleration of gravity)
The initial vertical velocity is
where the negative sign means the direction is downward.
The vertical position of the ball is given by
where
h = 4.50 m is the initial heigth of the ball when it starts falling down
The ball reaches the ground when y = 0, so we have:
This is a second-order equation; solving for t, we get
t = -1.18 s
t = 0.78 s
We discard the negative solution since it has no physical meaning, so we can say that the ball spent 0.78 s in the air.
2) Horizontal distance: 1.83 m
For this second part of the problem, we just have to consider the horizontal motion of the ball.
As we said previously, the motion of the ball along the horizontal direction is a uniform motion with constant velocity, which is given by
where u = 3.05 m/s is the initial speed and the angle of projection.
For a uniform motion, we can use the following relationship between distance covered and velocity:
and substituting t = 0.78 s, we find the total distance travelled along the horizontal direction by the ball before reaching the ground:
Answer:
10⁴¹ s quark top lives have been in the history of the universe.
Explanation:
You need to determine how many quark top lives there have been in the history of the universe, that is, what is the age of the universe divided by the lifetime of a top quark. Expressed in a formula, this is:
Yo know that the "Age of the universe" is 100,000,000,000,000,000 which can also be expressed as 10¹⁷ s .
You also know that the "Lifetime of a top quark" is 0.000000000000000000000001 which can also be expressed as 10⁻²⁴ s.
Then
Recalling that the result of dividing two powers of the same base is another power with the same base where the exponent is the subtraction of the initial exponents, it is possible to calculate this division as follows:
<u><em>t=10⁴¹ s</em></u>
So <u><em>10⁴¹ s quark top lives have been in the history of the universe.</em></u>