Answer:
13.5 ms
Explanation:
The sound wave travels with uniform motion in both cases, so the time taken to cover a distance d is given by:
![t=\frac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv%7D)
where
d is the distance to cover
v = 340 m/s is the speed of sound in air
So for the people across the newsroom,
d = 4.7 m
So the time taken is
![t=\frac{4.7}{340}=0.0138 s = 13.8 ms](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B4.7%7D%7B340%7D%3D0.0138%20s%20%3D%2013.8%20ms)
The radio waves instead travels with uniform motion at the speed of light:
![c=3.0\cdot 10^8 m/s](https://tex.z-dn.net/?f=c%3D3.0%5Ccdot%2010%5E8%20m%2Fs)
So the time taken for them is
![t=\frac{d}{c}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bc%7D)
where
d = 82 km = 82,000 m
is the distance of the people who are 82 km away. Substituting,
![t=\frac{82,000}{3.0\cdot 10^8}=0.27\cdot 10^{-3} s = 0.27 ms](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B82%2C000%7D%7B3.0%5Ccdot%2010%5E8%7D%3D0.27%5Ccdot%2010%5E%7B-3%7D%20s%20%3D%200.27%20ms)
Therefore, the difference in time is
![\Delta t = 13.8 ms - 0.27 ms = 13.5 ms](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%2013.8%20ms%20-%200.27%20ms%20%3D%2013.5%20ms)
<span>Every planet with an atmosphere has clouds. That includes the moon.</span>
Answer:
Gravitone
Explanation:
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravity. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The mass of the other block is ![m_1 = 81.14 \ kg](https://tex.z-dn.net/?f=m_1%20%3D%2081.14%20%5C%20kg)
Explanation:
From the question we are told that
Mass of the first block is ![m_1 = 100 \ kg](https://tex.z-dn.net/?f=m_1%20%3D%20100%20%5C%20%20kg)
The height is ![s = 1.0 \ m](https://tex.z-dn.net/?f=s%20%3D%20%201.0%20%5C%20%20m)
The time it takes it is
Generally from kinematic equation
![s = ut + \frac{1}{2} at^2](https://tex.z-dn.net/?f=s%20%3D%20%20ut%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20at%5E2)
Here u is the initial velocity which zero given that it was at rest initially
So
![s = 0 * t + \frac{1}{2} at^2](https://tex.z-dn.net/?f=s%20%3D%20%200%20%2A%20t%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20at%5E2)
=> ![s = \frac{1}{2} at^2](https://tex.z-dn.net/?f=s%20%3D%20%20%20%5Cfrac%7B1%7D%7B2%7D%20at%5E2)
=> ![1 = \frac{1}{2}* a * (1.40 )^2](https://tex.z-dn.net/?f=1%20%3D%20%20%20%5Cfrac%7B1%7D%7B2%7D%2A%20%20a%20%2A%20%20%281.40%20%29%5E2)
=> ![a = 1.0204 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%201.0204%20%5C%20%20m%2Fs%5E2)
Generally from the diagram the resultant force due to the weight of the first object and the tension on the string is mathematically represented as
![mg - T = ma](https://tex.z-dn.net/?f=mg%20-%20T%20%3D%20ma)
=> ![T = m g - ma](https://tex.z-dn.net/?f=T%20%20%3D%20%20m%20g%20-%20ma)
=> ![T = m(g - a)](https://tex.z-dn.net/?f=T%20%20%3D%20%20m%28g%20-%20a%29)
=> ![T = 877.96 \ N](https://tex.z-dn.net/?f=T%20%20%3D%20%20877.96%20%5C%20%20N)
Generally from the diagram the resultant force due to the weight of the second object and the tension on the string is mathematically represented as
![T - m_1g = m_1 a](https://tex.z-dn.net/?f=T%20-%20m_1g%20%20%3D%20%20m_1%20a)
=> ![877.96 = m_1 (a + g)](https://tex.z-dn.net/?f=877.96%20%20%3D%20%20m_1%20%28a%20%2B%20g%29)
=> ![877.96 = m_1 (1.0204 + 9.8 )](https://tex.z-dn.net/?f=877.96%20%20%3D%20%20m_1%20%281.0204%20%20%2B%209.8%20%29)
=> ![m_1 = 81.14 \ kg](https://tex.z-dn.net/?f=m_1%20%3D%2081.14%20%5C%20kg)
Answer:
7.5 units
13 units
Explanation:
![|v|=5\ \text{units}](https://tex.z-dn.net/?f=%7Cv%7C%3D5%5C%20%5Ctext%7Bunits%7D)
![|u|=3\ \text{units}](https://tex.z-dn.net/?f=%7Cu%7C%3D3%5C%20%5Ctext%7Bunits%7D)
= Angle between the vectors = ![60^{\circ}](https://tex.z-dn.net/?f=60%5E%7B%5Ccirc%7D)
Scalar product is given by
![u\cdot v=|u||v|\cos\theta\\ =3\cdot 5\cdot \cos60^{\circ}\\ =7.5\ \text{units}](https://tex.z-dn.net/?f=u%5Ccdot%20v%3D%7Cu%7C%7Cv%7C%5Ccos%5Ctheta%5C%5C%20%3D3%5Ccdot%205%5Ccdot%20%5Ccos60%5E%7B%5Ccirc%7D%5C%5C%20%3D7.5%5C%20%5Ctext%7Bunits%7D)
The scalar product of the vectors is 7.5 units.
Vector product is given by
![u\times v=|u||v|\sin\theta\\ =3\times 5\sin60^{\circ}\\ =13\ \text{units}](https://tex.z-dn.net/?f=u%5Ctimes%20v%3D%7Cu%7C%7Cv%7C%5Csin%5Ctheta%5C%5C%20%3D3%5Ctimes%205%5Csin60%5E%7B%5Ccirc%7D%5C%5C%20%3D13%5C%20%5Ctext%7Bunits%7D)
The vector product of the vectors is 13 units.