Answer:
voltage divider, R₂ = 1000 R₁
measuring the output in the resistance R₁
Explanation:
Let's analyze the situation, in an op amp in open gain loop, the gain is maximum G = 10⁶ V / V
in this case the signal generator gives a minimum wave of 1 10⁻³ V, after passing through the amplified it becomes 10³ V which saturates the oscilloscope.
To solve this problem we must use a simple voltage divider, for this we use the fact that in a series circuit the voltage is the sum of the voltages of each element.
If we use two resistors whose relationship is
R₂ / R₁ = 10³
R₂ = 1000 R₁
When measuring the output in the resistance R₁ we have the desired divider, with a tolerance range, for the minimum output of the generator (1 10⁻³V) we have a reading of V = 1 V in the oscilloscope, for which we can use voltage up to 10V on the generator
Answer:
53.895 m.
Explanation:
Using the equation of motion,
v² = u² + 2as .............. Equation 1
Where v = final velocity of the swan, u = initial velocity of the swan, a = acceleration of the swan, s = distance covered by the swan.
make s the subject of the equation,
s = (v² - u²)/2a----------- Equation 2
Given: v = 6.4 m/s, u = 0 m/s ( from rest) a = 0.380 m/s².
Substitute into equation 2
s = (6.4²-0²)/(2×0.380)
s = 40.96/0.76
s = 53.895 m.
Hence the swan will travel 53.895 m before becoming airborne.
Answer:t=0.3253 s
Explanation:
Given
speed of balloon is ![u=3\ m/s](https://tex.z-dn.net/?f=u%3D3%5C%20m%2Fs)
speed of camera ![u_1=20\ m/s](https://tex.z-dn.net/?f=u_1%3D20%5C%20m%2Fs)
Initial separation between camera and balloon is ![d_o=5\ m](https://tex.z-dn.net/?f=d_o%3D5%5C%20m)
Suppose after t sec of throw camera reach balloon then,
distance travel by balloon is
![s=ut](https://tex.z-dn.net/?f=s%3Dut)
![s=3\times t](https://tex.z-dn.net/?f=s%3D3%5Ctimes%20t)
and distance travel by camera to reach balloon is
![s_1=ut+\frac{1}{2}at^2](https://tex.z-dn.net/?f=s_1%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
![s_1=20\times t-\frac{1}{2}gt^2](https://tex.z-dn.net/?f=s_1%3D20%5Ctimes%20t-%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
Now
![\Rightarrow s_1=5+s](https://tex.z-dn.net/?f=%5CRightarrow%20s_1%3D5%2Bs)
![\Rightarrow 20\times t-\frac{1}{2}gt^2 =5+3t](https://tex.z-dn.net/?f=%5CRightarrow%2020%5Ctimes%20t-%5Cfrac%7B1%7D%7B2%7Dgt%5E2%20%3D5%2B3t)
![\Rightarrow 5t^2-17t+5=0](https://tex.z-dn.net/?f=%5CRightarrow%205t%5E2-17t%2B5%3D0)
![\Rightarrow t=\dfrac{17\pm \sqrt{17^2-4(5)(5)}}{2\times 5}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cdfrac%7B17%5Cpm%20%5Csqrt%7B17%5E2-4%285%29%285%29%7D%7D%7B2%5Ctimes%205%7D)
![\Rightarrow t=\dfrac{17\pm 13.747}{10}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cdfrac%7B17%5Cpm%2013.747%7D%7B10%7D)
![\Rightarrow t=0.3253\ s\ \text{and}\ t=3.07\ s](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D0.3253%5C%20s%5C%20%5Ctext%7Band%7D%5C%20t%3D3.07%5C%20s)
There are two times when camera reaches the same level as balloon and the smaller time is associated with with the first one .
(b)When passenger catches the camera time is ![t=0.3253\ s](https://tex.z-dn.net/?f=t%3D0.3253%5C%20s)
velocity is given by
![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
![v=20-10\times 0.3253](https://tex.z-dn.net/?f=v%3D20-10%5Ctimes%200.3253)
![v=16.747\ m/s](https://tex.z-dn.net/?f=v%3D16.747%5C%20m%2Fs)
and position of camera is same as of balloon so
Position is ![=5+3\times 0.3253](https://tex.z-dn.net/?f=%3D5%2B3%5Ctimes%200.3253)
![=5.975\approx 6\ m](https://tex.z-dn.net/?f=%3D5.975%5Capprox%206%5C%20m)
![1.984 \times 10^{-11} \mathrm{N} \text { is the force of gravity exerted on the jar of pickles. }](https://tex.z-dn.net/?f=1.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D%20%5Ctext%20%7B%20is%20the%20force%20of%20gravity%20exerted%20on%20the%20jar%20of%20pickles.%20%7D)
<u>Explanation</u>:
According to Newton's third law that each force has an equal and opposite reaction force in this case both of the jars will exert the same force an each other
. The force is given by
![\mathrm{F}=\frac{G \times M_{1} \times M_{2}}{r^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7BG%20%5Ctimes%20M_%7B1%7D%20%5Ctimes%20M_%7B2%7D%7D%7Br%5E%7B2%7D%7D)
Where, F = force,
,
,
and Distance(r) = 0.42 m.
Substitute the values in the formula.
![\mathrm{F}=\frac{6.67 \times 10^{-11} \times 0.17 \times 0.31}{0.42^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7B6.67%20%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%200.17%20%5Ctimes%200.31%7D%7B0.42%5E%7B2%7D%7D)
![\mathrm{F}=\frac{3.51 \times 10^{-12}}{0.176}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7B3.51%20%5Ctimes%2010%5E%7B-12%7D%7D%7B0.176%7D)
![\mathrm{F}=1.984 \times 10^{-11} \mathrm{N}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D1.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D)
![\text { The force of gravity exerted on the jar of pickles is } 1.984 \times 10^{-11} \mathrm{N} \text { . }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20force%20of%20gravity%20exerted%20on%20the%20jar%20of%20pickles%20is%20%7D%201.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D%20%5Ctext%20%7B%20.%20%7D)
Answer: 0 km/h
Explanation:
As a vector, the plane's velocity is 100 km/h (west) - 100 km/h (east) = 0 km/m.
To an observer on the ground, the plane will be standing still.