Answer:
The rate of change of the distance between the helicopter and yourself (in ft/s) after 5 s is
ft/ sec
Explanation:
Given:
h(t) = 25 ft/sec
x(t) = 10 ft/ sec
h(5) = 25 ft/sec . 5 = 125 ft
x(5) = 10 ft/sec . 5 = 50 ft
Now we can calculate the distance between the person and the helicopter by using the Pythagorean theorem
![D(t) = \sqrt{h^2 + x^2}](https://tex.z-dn.net/?f=D%28t%29%20%3D%20%5Csqrt%7Bh%5E2%20%2B%20x%5E2%7D)
Lets find the derivative of distance with respect to time
![\frac{dD}{dt} (t) = \frac{2h \cdot \frac{dh}{dt} +2x \cdot\frac{dx}{dt}} {2\sqrt{h^2 + x^2}}](https://tex.z-dn.net/?f=%5Cfrac%7BdD%7D%7Bdt%7D%20%28t%29%20%20%3D%20%5Cfrac%7B2h%20%5Ccdot%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B2x%20%5Ccdot%5Cfrac%7Bdx%7D%7Bdt%7D%7D%20%7B2%5Csqrt%7Bh%5E2%20%2B%20x%5E2%7D%7D)
Substituting the values of h(t) and x(t) and simplifying we get,
![\frac{dD}{dt}(t) = \frac{50t \cdot \frac{dh}{dt} + 20 \cdot \frac{dx}dt}{2\sqrt{625\cdot t^2 + 100 \cdot t^2}}](https://tex.z-dn.net/?f=%5Cfrac%7BdD%7D%7Bdt%7D%28t%29%20%3D%20%5Cfrac%7B50t%20%5Ccdot%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%2020%20%5Ccdot%20%5Cfrac%7Bdx%7Ddt%7D%7B2%5Csqrt%7B625%5Ccdot%20t%5E2%20%2B%20100%20%5Ccdot%20t%5E2%7D%7D)
![\frac{dh}{dt} = 25ft/sec](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%2025ft%2Fsec)
![\frac{dx}{dt} = 10 ft/sec](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%2010%20ft%2Fsec)
=
=
ft / sec
Answer:
The speed of transverse waves in this string is 519.61 m/s.
Explanation:
Given that,
Mass per unit length = 5.00 g/m
Tension = 1350 N
We need to calculate the speed of transverse waves in this string
Using formula of speed of the transverse waves
![v=\sqrt{\dfrac{T}{\mu}}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cdfrac%7BT%7D%7B%5Cmu%7D%7D)
Where,
= mass per unit length
T = tension
Put the value into the formula
![v = \sqrt{\dfrac{1350}{5.00\times10^{-3}}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cdfrac%7B1350%7D%7B5.00%5Ctimes10%5E%7B-3%7D%7D%7D)
![v =519.61\ m/s](https://tex.z-dn.net/?f=v%20%3D519.61%5C%20m%2Fs)
Hence, The speed of transverse waves in this string is 519.61 m/s.
Given :
The focal length of a concave mirror is 18 cm.
To Find :
The radius of curvature of the concave mirror.
Solution :
We know,
![\text{Focal length}=\dfrac{\text{Radius of curvature}}{2}\\\\F=\dfrac{R}{2}\\\\R = 18\times 2\ cm\\\\R = 36 \ cm](https://tex.z-dn.net/?f=%5Ctext%7BFocal%20length%7D%3D%5Cdfrac%7B%5Ctext%7BRadius%20of%20curvature%7D%7D%7B2%7D%5C%5C%5C%5CF%3D%5Cdfrac%7BR%7D%7B2%7D%5C%5C%5C%5CR%20%3D%2018%5Ctimes%202%5C%20cm%5C%5C%5C%5CR%20%3D%2036%20%5C%20cm)
Therefore, the radius of curvature of concave mirror is 36 cm.
Hence, this is the required solution.
Answer:
Explanation:
Given
mass of wheel m=13 kg
radius of wheel=1.8 m
N=469 rev/min
![\omega =\frac{2\pi \times 469}{60}=49.11 rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%5Cfrac%7B2%5Cpi%20%5Ctimes%20469%7D%7B60%7D%3D49.11%20rad%2Fs)
t=16 s
Angular deceleration in 16 s
![\omega =\omega _0+\alpha \cdot t](https://tex.z-dn.net/?f=%5Comega%20%3D%5Comega%20_0%2B%5Calpha%20%5Ccdot%20t)
![\alpha =\frac{\omega }{t}=\frac{49.11}{16}=3.069 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D%5Cfrac%7B%5Comega%20%7D%7Bt%7D%3D%5Cfrac%7B49.11%7D%7B16%7D%3D3.069%20rad%2Fs%5E2)
Moment of Inertia ![I=mr^2=13\times 1.8^2=42.12 kg-m^2](https://tex.z-dn.net/?f=I%3Dmr%5E2%3D13%5Ctimes%201.8%5E2%3D42.12%20kg-m%5E2)
Change in kinetic energy =Work done
Change in kinetic Energy![=\frac{I\omega ^2}{2}-\frac{I\omega _0^2}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7BI%5Comega%20%5E2%7D%7B2%7D-%5Cfrac%7BI%5Comega%20_0%5E2%7D%7B2%7D)
![\Delta KE=\frac{42.12\times 49.11^2}{2}=50,792.34 J](https://tex.z-dn.net/?f=%5CDelta%20KE%3D%5Cfrac%7B42.12%5Ctimes%2049.11%5E2%7D%7B2%7D%3D50%2C792.34%20J)
(a)Work done =50.79 kJ
(b)Average Power
![P_{avg}=\frac{E}{t}=\frac{50.792}{16}=3.174 kW](https://tex.z-dn.net/?f=P_%7Bavg%7D%3D%5Cfrac%7BE%7D%7Bt%7D%3D%5Cfrac%7B50.792%7D%7B16%7D%3D3.174%20kW)
The angular velocity, ω=
2π/t; t = 24 hrs = 24 x 3600 seconds = 86400 s
ω = 7.27 x 10⁻⁵
v = ωr
= 7.27 x 10⁻⁵ x 3242.8 x 1.6 x 1000 (converting miles to meters)
= 377.2 m/s