Answer:
The velocity is ![v = 4.76 \ m/s](https://tex.z-dn.net/?f=v%20%3D%204.76%20%5C%20m%2Fs)
Explanation:
From the question we are told that
The first distance is ![d_1 = 4.0 \ km = 4000 \ m](https://tex.z-dn.net/?f=d_1%20%20%3D%20%204.0%20%5C%20km%20%20%3D%20%204000%20%5C%20m)
The first speed is ![v_1 = 5.0 \ m/s](https://tex.z-dn.net/?f=v_1%20%3D%20%205.0%20%5C%20m%2Fs)
The second distance is ![d_2 = 1.0 \ km = 1000 \ m](https://tex.z-dn.net/?f=d_2%20%20%3D%20%201.0%20%5C%20km%20%20%3D%20%201000%20%5C%20m)
The second speed is ![v_2 = 4.0 \ m/s](https://tex.z-dn.net/?f=v_2%20%20%3D%20%204.0%20%5C%20m%2Fs)
Generally the time taken for first distance is
![t_1 = \frac{d_1 }{v_1 }](https://tex.z-dn.net/?f=t_1%20%3D%20%20%5Cfrac%7Bd_1%20%7D%7Bv_1%20%7D)
![t_1 = \frac{4000}{5}](https://tex.z-dn.net/?f=t_1%20%3D%20%20%5Cfrac%7B4000%7D%7B5%7D)
![t_1 = 800 \ s](https://tex.z-dn.net/?f=t_1%20%3D%20%20800%20%5C%20s)
The time taken for second distance is
![t_1 = \frac{d_2 }{v_2 }](https://tex.z-dn.net/?f=t_1%20%3D%20%20%5Cfrac%7Bd_2%20%7D%7Bv_2%20%7D)
![t_1 = \frac{1000}{4}](https://tex.z-dn.net/?f=t_1%20%3D%20%20%5Cfrac%7B1000%7D%7B4%7D)
![t_1 = 250 \ s](https://tex.z-dn.net/?f=t_1%20%3D%20%20250%20%5C%20s)
The total time is mathematically represented as
![t = t_1 + t_2](https://tex.z-dn.net/?f=t%20%3D%20%20t_1%20%2B%20t_2)
=> ![t = 800 + 250](https://tex.z-dn.net/?f=t%20%3D%20%20800%20%2B%20250)
=> ![t = 1050 \ s](https://tex.z-dn.net/?f=t%20%3D%20%201050%20%5C%20s)
Generally the constant velocity that would let her finish at the same time is mathematically represented as
![v = \frac{d_1 + d_2}{t }](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7Bd_1%20%2B%20d_2%7D%7Bt%20%7D)
=> ![v = \frac{4000 + 1000}{1050 }](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B4000%20%2B%201000%7D%7B1050%20%7D)
=> ![v = 4.76 \ m/s](https://tex.z-dn.net/?f=v%20%3D%204.76%20%5C%20m%2Fs)
Th correct option is D.
A generator operates by converting mechanical energy into electrical energy by rotating coils of wire around magnetic field. There are two types of generator, a direct current generator and an alternating current generator.
Expand each vector into their component forms:
![\vec A=(4.5\,\mathrm N)(\cos\theta_A\,\vec\imath+\sin\theta_A\,\vec\jmath)=(2.58\,\vec\imath+3.69\,\vec\jmath)\,\mathrm N](https://tex.z-dn.net/?f=%5Cvec%20A%3D%284.5%5C%2C%5Cmathrm%20N%29%28%5Ccos%5Ctheta_A%5C%2C%5Cvec%5Cimath%2B%5Csin%5Ctheta_A%5C%2C%5Cvec%5Cjmath%29%3D%282.58%5C%2C%5Cvec%5Cimath%2B3.69%5C%2C%5Cvec%5Cjmath%29%5C%2C%5Cmathrm%20N)
Similarly,
![\vec B=(-1.23\,\vec\imath+0.860\,\vec\jmath)\,\mathrm N](https://tex.z-dn.net/?f=%5Cvec%20B%3D%28-1.23%5C%2C%5Cvec%5Cimath%2B0.860%5C%2C%5Cvec%5Cjmath%29%5C%2C%5Cmathrm%20N)
![\vec C=(-3.44\,\vec\imath-4.91\,\vec\jmath)\,\mathrm N](https://tex.z-dn.net/?f=%5Cvec%20C%3D%28-3.44%5C%2C%5Cvec%5Cimath-4.91%5C%2C%5Cvec%5Cjmath%29%5C%2C%5Cmathrm%20N)
Then assuming the resultant vector
is the sum of these three vectors, we have
![\vec R=\vec A+\vec B+\vec C](https://tex.z-dn.net/?f=%5Cvec%20R%3D%5Cvec%20A%2B%5Cvec%20B%2B%5Cvec%20C)
![\vec R=(-2.09\,\vec\imath-0.368\,\vec\jmath)\,\mathrm N](https://tex.z-dn.net/?f=%5Cvec%20R%3D%28-2.09%5C%2C%5Cvec%5Cimath-0.368%5C%2C%5Cvec%5Cjmath%29%5C%2C%5Cmathrm%20N)
and so
has magnitude
![\|\vec R\|=\sqrt{(-2.09)^2+(-0.368)^2}\,\mathrm N\approx2.12\,\mathrm N](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20R%5C%7C%3D%5Csqrt%7B%28-2.09%29%5E2%2B%28-0.368%29%5E2%7D%5C%2C%5Cmathrm%20N%5Capprox2.12%5C%2C%5Cmathrm%20N)
and direction
such that
![\tan\theta_R=\dfrac{-0.368}{-2.09}\implies\theta_R=-170^\circ=190^\circ](https://tex.z-dn.net/?f=%5Ctan%5Ctheta_R%3D%5Cdfrac%7B-0.368%7D%7B-2.09%7D%5Cimplies%5Ctheta_R%3D-170%5E%5Ccirc%3D190%5E%5Ccirc)
Answer:
C. 30.6m
Explanation:
To find the height of the tower, we are to use Newtons law of motion to solve this problem. Since the penny is falling from the top of the tower, it is acted by the acceleration due to gravity. The formula to be used is:
![H=ut+\frac{1}{2}gt^2](https://tex.z-dn.net/?f=H%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
Where H is the height of the tower, t is the time taken to hit the ground, u is the initial velocity and g is the acceleration due to gravity.
Given that, t = 2.5 s, g =9.8 m/s², u = 0 m/s (at the top of tower)
![H=ut+\frac{1}{2}gt^2\\\\H=0(2.5)+ \frac{1}{2}(9.8)(2.5)^2\\\\H=30.6\ m](https://tex.z-dn.net/?f=H%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dgt%5E2%5C%5C%5C%5CH%3D0%282.5%29%2B%20%5Cfrac%7B1%7D%7B2%7D%289.8%29%282.5%29%5E2%5C%5C%5C%5CH%3D30.6%5C%20m)