Answer:
a) Acceleration of the car is given as
![a_{car} = -21 m/s^2](https://tex.z-dn.net/?f=a_%7Bcar%7D%20%3D%20-21%20m%2Fs%5E2)
b) Acceleration of the truck is given as
![a_{truck} = 10.15 m/s^2](https://tex.z-dn.net/?f=a_%7Btruck%7D%20%3D%2010.15%20m%2Fs%5E2)
Explanation:
As we know that there is no external force in the direction of motion of truck and car
So here we can say that the momentum of the system before and after collision must be conserved
So here we will have
![m_1v_1 + m_2v_2 = (m_1 + m_2)v](https://tex.z-dn.net/?f=m_1v_1%20%2B%20m_2v_2%20%3D%20%28m_1%20%2B%20m_2%29v)
now we have
![1400 (6.32) + 2900(0) = (1400 + 2900) v](https://tex.z-dn.net/?f=1400%20%286.32%29%20%2B%202900%280%29%20%3D%20%281400%20%2B%202900%29%20v)
![v = 2.06 m/s](https://tex.z-dn.net/?f=v%20%3D%202.06%20m%2Fs)
a) For acceleration of car we know that it is rate of change in velocity of car
so we have
![a_{car} = \frac{v_f - v_i}{t}](https://tex.z-dn.net/?f=a_%7Bcar%7D%20%3D%20%5Cfrac%7Bv_f%20-%20v_i%7D%7Bt%7D)
![a_{car} = \frac{2.06 - 6.32}{0.203}](https://tex.z-dn.net/?f=a_%7Bcar%7D%20%3D%20%5Cfrac%7B2.06%20-%206.32%7D%7B0.203%7D)
![a_{car} = -21 m/s^2](https://tex.z-dn.net/?f=a_%7Bcar%7D%20%3D%20-21%20m%2Fs%5E2)
b) For acceleration of truck we will find the rate of change in velocity of the truck
so we have
![a_{truck} = \frac{v_f - v_i}{t}](https://tex.z-dn.net/?f=a_%7Btruck%7D%20%3D%20%5Cfrac%7Bv_f%20-%20v_i%7D%7Bt%7D)
![a_{truck} = \frac{2.06 - 0}{0.203}](https://tex.z-dn.net/?f=a_%7Btruck%7D%20%3D%20%5Cfrac%7B2.06%20-%200%7D%7B0.203%7D)
![a_{truck} = 10.15 m/s^2](https://tex.z-dn.net/?f=a_%7Btruck%7D%20%3D%2010.15%20m%2Fs%5E2)
Answer:
![1.91773\times 10^{37}\ kg](https://tex.z-dn.net/?f=1.91773%5Ctimes%2010%5E%7B37%7D%5C%20kg)
Explanation:
v = Orbital speed = 130 km/s
d = Diameter = 16 ly
r = Radius = ![\dfrac{d}{2}=\dfrac{16}{2}=8\ ly](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7B2%7D%3D%5Cdfrac%7B16%7D%7B2%7D%3D8%5C%20ly)
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
![1\ ly=9.461\times 10^{15}\ m](https://tex.z-dn.net/?f=1%5C%20ly%3D9.461%5Ctimes%2010%5E%7B15%7D%5C%20m)
As the centripetal force balances the gravitational energy we have the following relation
![\dfrac{GMm}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow M=\dfrac{v^2r}{G}\\\Rightarrow M=\dfrac{130000^2\times 8\times 9.461\times 10^{15}}{6.67\times 10^{-11}}\\\Rightarrow M=1.91773\times 10^{37}\ kg](https://tex.z-dn.net/?f=%5Cdfrac%7BGMm%7D%7Br%5E2%7D%3D%5Cdfrac%7Bmv%5E2%7D%7Br%7D%5C%5C%5CRightarrow%20M%3D%5Cdfrac%7Bv%5E2r%7D%7BG%7D%5C%5C%5CRightarrow%20M%3D%5Cdfrac%7B130000%5E2%5Ctimes%208%5Ctimes%209.461%5Ctimes%2010%5E%7B15%7D%7D%7B6.67%5Ctimes%2010%5E%7B-11%7D%7D%5C%5C%5CRightarrow%20M%3D1.91773%5Ctimes%2010%5E%7B37%7D%5C%20kg)
Mass of the the massive object at the center of the Milky Way galaxy is ![1.91773\times 10^{37}\ kg](https://tex.z-dn.net/?f=1.91773%5Ctimes%2010%5E%7B37%7D%5C%20kg)
Well if the child weighs 44 kg then 44 kg. Do you mean if they weigh 44 kg in space to earth?
P always P because P is an awkward Dorian letter that can always be trusted