Answer:
a)![t=5.5\mu s](https://tex.z-dn.net/?f=t%3D5.5%5Cmu%20s)
b)![\Delta t'=12.5\mu s](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D12.5%5Cmu%20s)
Explanation:
a) Let's use the constant velocity equation:
![v=\frac{\Delta x}{\Delta t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B%5CDelta%20x%7D%7B%5CDelta%20t%7D)
- v is the speed of the muon. 0.9*c
- c is the speed of light 3*10⁸ m/s
![t=\frac{\Delta x}{v}=\frac{1500}{0.9*(3*10^{8})}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5CDelta%20x%7D%7Bv%7D%3D%5Cfrac%7B1500%7D%7B0.9%2A%283%2A10%5E%7B8%7D%29%7D)
![t=5.5\mu s](https://tex.z-dn.net/?f=t%3D5.5%5Cmu%20s)
b) Here we need to use Lorentz factor because the speed of the muon is relativistic. Hence the time in the rest frame is the product of the Lorentz factor times the time in the inertial frame.
![\Delta t'=\gamma\Delta t](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D%5Cgamma%5CDelta%20t)
![\gamma =\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}](https://tex.z-dn.net/?f=%5Cgamma%20%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D)
v is the speed of muon (0.9c)
Therefore the time in the rest frame will be:
![\Delta t'=\frac{1}{\sqrt{1-\frac{(0.9c)^{2}}{c^{2}}}}\Delta t](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-%5Cfrac%7B%280.9c%29%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D%5CDelta%20t)
![\Delta t'=\frac{1}{\sqrt{1-0.9^{2}}}\Delta t](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-0.9%5E%7B2%7D%7D%7D%5CDelta%20t)
![\Delta t'=\frac{1}{0.44}\Delta t](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D%5Cfrac%7B1%7D%7B0.44%7D%5CDelta%20t)
No we use the value of Δt calculated in a)
![\Delta t'=2.27*5.5=12.5\mu s](https://tex.z-dn.net/?f=%5CDelta%20t%27%3D2.27%2A5.5%3D12.5%5Cmu%20s)
I hope it helps you!
Answer:period, spring constant, radius of circular part, velocity of the test mass, mass of the test-mass, mass of the hanging mass
Explanation:
V o = 6 m/s,
t = 2 s
v = 10 m/s
v = v o + a t
a t = v - v o
a = ( v - v o ) / t
a = ( 10 m/s - 6 m/s ) / 2 s = 4 m/s / 2 s = 2 m/s²
Answer:
The runner`s acceleration is 2 m/s².
Position of B :
x = 4.66*cos 30 = 4.036
y = 3-4.66*sin 30 = 3-2.33 = 0.67
BC = √y^2+(x-1)^2 = √0.67^2+3.036^2 = 3.109
heading = arctan y/(x-1) = arctan 0.67/(3.036) = 12.44° south of west
hope this helps :)
Answer: 33
Explanation:
12+3=15, so in 3 years time Ruto will be 15.
Because 15 is said to be 1/3 times his fathers present age (x), you can plug that into an equation.
15=1/3(x)
Then solve the equation.
(3)15=[1/3(x)]•3
45=x
His father is currently 45, so if you subtract 12 from that, you get 33.
Ruto’s father was 33 years old 12 years ago.