Answer:
42.11 years old
Explanation:
Given that:
In 2000, a 20-year-old astronaut left Earth to explore the galaxy; her spaceship travels at 2.5 x 10^8 m/s. She returns in 2040
To find her age we use:
![\Delta t_m=\frac{\Delta t_s}{\sqrt{1-\frac{v^2}{c^2} } }\\](https://tex.z-dn.net/?f=%5CDelta%20t_m%3D%5Cfrac%7B%5CDelta%20t_s%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D%5C%5C)
Δtm is time interval for the observer stationary relative to the sequence of
events = 2040 - 2000 = 40 years
Δts is is the time interval for an observer moving with a speed v relative to the sequence of event
v = velocity = 2.5 x 10^8 m/s
c = speed of light = 3 x 10^8 m/s
![\Delta t_s=\Delta t_m}{\sqrt{1-\frac{v^2}{c^2} } }\\\Delta t_s=40\sqrt{1-\frac{(2.5*10^8)^2}{(3*10^8)^2}}\\\Delta t_s=22.11\ yr](https://tex.z-dn.net/?f=%5CDelta%20t_s%3D%5CDelta%20t_m%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D%5C%5C%5CDelta%20t_s%3D40%5Csqrt%7B1-%5Cfrac%7B%282.5%2A10%5E8%29%5E2%7D%7B%283%2A10%5E8%29%5E2%7D%7D%5C%5C%5CDelta%20t_s%3D22.11%5C%20yr)
Here age in 2000 is 20 year, therefore when she appear she would be 20 year + 22.11 year = 42.11 years old
The centripetal force (of gravity) on a satellite in orbit is an
unbalanced force (because there's no equal force pulling
the satellite away from Earth), changes the direction of the
satellite (into a closed orbit instead of a straight line), and
always acts toward the center of whatever curve the satellite
happens to be on at the moment.
The angular frequency of the wave is determined as 75.4 rad/s.
<h3>
What is wave function?</h3>
A wave function is a mathematical equation for the motion of the wave.
y(x, t) = A sin(kx + ωt + Φ)
where;
- ω is angular speed
- k is angular wavenumber
- Φ is phase angle
<h3>What is angular frequency?</h3>
The angular frequency is the angular displacement of any wave element per unit of time or the rate of change of the waveform phase.
<h3>Angular frequency</h3>
ω = 2πf
ω = 2π(12)
ω = 75.4 rad/s
Thus, the angular frequency of the wave is determined as 75.4 rad/s.
Learn more about angular frequency here: brainly.com/question/3654452
#SPJ4
Answer:
240 ft
Explanation:
t = Time taken
u = Initial velocity = 96 ft/s
v = Final velocity
s = Displacement
a = Acceleration = 12 m/s² on Mars 32 ft/s² on Earth negative due to upward direction
Mars
![s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -12\times t^2\\\Rightarrow s=96t-6t^2\ ft](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%20s%3D96%5Ctimes%20t%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-12%5Ctimes%20t%5E2%5C%5C%5CRightarrow%20s%3D96t-6t%5E2%5C%20ft)
Earth
![s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -32\times t^2\\\Rightarrow s=96t-16t^2\ ft](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%20s%3D96%5Ctimes%20t%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-32%5Ctimes%20t%5E2%5C%5C%5CRightarrow%20s%3D96t-16t%5E2%5C%20ft)
Differentiating the first equation with respect to time we get
![\frac{ds}{dt}=96-12t](https://tex.z-dn.net/?f=%5Cfrac%7Bds%7D%7Bdt%7D%3D96-12t)
Equating with zero
![0=96-12t\\\Rightarrow t=\frac{96}{12}=8\ s](https://tex.z-dn.net/?f=0%3D96-12t%5C%5C%5CRightarrow%20t%3D%5Cfrac%7B96%7D%7B12%7D%3D8%5C%20s)
Differentiating the second equation with respect to time we get
Equating with zero
![0=96-32t\\\Rightarrow t=\frac{96}{32}=3\ s](https://tex.z-dn.net/?f=0%3D96-32t%5C%5C%5CRightarrow%20t%3D%5Cfrac%7B96%7D%7B32%7D%3D3%5C%20s)
Applying the time taken to the above equations, we get
![s=96t-6t^2\ ft\\\Rightarrow s=96\times 8-6\times 8^2\\\Rightarrow s=384](https://tex.z-dn.net/?f=s%3D96t-6t%5E2%5C%20ft%5C%5C%5CRightarrow%20s%3D96%5Ctimes%208-6%5Ctimes%208%5E2%5C%5C%5CRightarrow%20s%3D384)
![s=96t-16t^2\\\Rightarrow s=96\times 3-16\times 3^2\\\Rightarrow s=144](https://tex.z-dn.net/?f=s%3D96t-16t%5E2%5C%5C%5CRightarrow%20s%3D96%5Ctimes%203-16%5Ctimes%203%5E2%5C%5C%5CRightarrow%20s%3D144)
Difference in height = 384-144 = 240 ft
The stone will travel 240 ft higher on Mars