An electromagnetic wave of a frequency between about 104<span> and 10</span>11<span> or 10</span>12<span> Hz, as used for long-distance communication</span>
Answer:
(a) 1.21 m/s
(b) 2303.33 J, 152.27 J
Explanation:
m1 = 95 kg, u1 = - 3.750 m/s, m2 = 113 kg, u2 = 5.38 m/s
(a) Let their velocity after striking is v.
By use of conservation of momentum
Momentum before collision = momentum after collision
m1 x u1 + m2 x u2 = (m1 + m2) x v
- 95 x 3.75 + 113 x 5.38 = (95 + 113) x v
v = ( - 356.25 + 607.94) / 208 = 1.21 m /s
(b) Kinetic energy before collision = 1/2 m1 x u1^2 + 1/2 m2 x u2^2
= 0.5 ( 95 x 3.750 x 3.750 + 113 x 5.38 x 5.38)
= 0.5 (1335.94 + 3270.7) = 2303.33 J
Kinetic energy after collision = 1/2 (m1 + m2) v^2
= 0.5 (95 + 113) x 1.21 x 1.21 = 152.27 J
Answer
a) For the rock
![\dfrac{v_t^2sin 2\theta}{g} = \dfrac{v_t^2sin^2\theta}{2g}](https://tex.z-dn.net/?f=%5Cdfrac%7Bv_t%5E2sin%202%5Ctheta%7D%7Bg%7D%20%3D%20%5Cdfrac%7Bv_t%5E2sin%5E2%5Ctheta%7D%7B2g%7D)
![2sin\thetacos\theta = \dfrac{sin^2\theta}{2}](https://tex.z-dn.net/?f=2sin%5Cthetacos%5Ctheta%20%3D%20%5Cdfrac%7Bsin%5E2%5Ctheta%7D%7B2%7D)
![2cos\theta = \dfrac{sin\theta}{2}](https://tex.z-dn.net/?f=2cos%5Ctheta%20%3D%20%5Cdfrac%7Bsin%5Ctheta%7D%7B2%7D)
![tan\theta = 4](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%204)
![\theta = tan^{-1} 4](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%204)
![\theta = 76^0](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2076%5E0)
b)
for maximum range
![\dfrac{d_{max}}{d}=\dfrac{(v_tcos 45^0)(2v_tsin 45^0)g}{(v_tcos 76^0)(2v_tsin 76^0)g}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_%7Bmax%7D%7D%7Bd%7D%3D%5Cdfrac%7B%28v_tcos%2045%5E0%29%282v_tsin%2045%5E0%29g%7D%7B%28v_tcos%2076%5E0%29%282v_tsin%2076%5E0%29g%7D)
![\dfrac{d_{max}}{d}=\dfrac{0.707\times 0.707)}{0.97\times 0.242}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_%7Bmax%7D%7D%7Bd%7D%3D%5Cdfrac%7B0.707%5Ctimes%200.707%29%7D%7B0.97%5Ctimes%200.242%7D)
![\dfrac{d_{max}}{d}=2.129](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_%7Bmax%7D%7D%7Bd%7D%3D2.129)
![d_{max}=2.129 d](https://tex.z-dn.net/?f=d_%7Bmax%7D%3D2.129%20d)
c) The value of θ is the same on every planet as g divides out.
Answer: 110000
Explanation:
26/9=30.5555555556
30.5555555556 x 60=1833.33333333
110000 x 60=110000
The answer is 100mm/s. I hope this helps :)