2.71 m/s fast Hans is moving after the collision.
<u>Explanation</u>:
Given that,
Mass of Jeremy is 120 kg (
)
Speed of Jeremy is 3 m/s (
)
Speed of Jeremy after collision is (
) -2.5 m/s
Mass of Hans is 140 kg (
)
Speed of Hans is -2 m/s (
)
Speed of Hans after collision is (
)
Linear momentum is defined as “mass time’s speed of the vehicle”. Linear momentum before the collision of Jeremy and Hans is
= ![=\mathrm{M}_{1} \times \mathrm{V}_{\mathrm{J}}+\mathrm{M}_{\mathrm{H}} \times \mathrm{V}_{\mathrm{H}}](https://tex.z-dn.net/?f=%3D%5Cmathrm%7BM%7D_%7B1%7D%20%5Ctimes%20%5Cmathrm%7BV%7D_%7B%5Cmathrm%7BJ%7D%7D%2B%5Cmathrm%7BM%7D_%7B%5Cmathrm%7BH%7D%7D%20%5Ctimes%20%5Cmathrm%7BV%7D_%7B%5Cmathrm%7BH%7D%7D)
Substitute the given values,
= 120 × 3 + 140 × (-2)
= 360 + (-280)
= 80 kg m/s
Linear momentum after the collision of Jeremy and Hans is
= ![=\mathrm{M}_{\mathrm{J}} \times \mathrm{V}_{\mathrm{JA}}+\mathrm{M}_{\mathrm{H}} \times \mathrm{V}_{\mathrm{HA}}](https://tex.z-dn.net/?f=%3D%5Cmathrm%7BM%7D_%7B%5Cmathrm%7BJ%7D%7D%20%5Ctimes%20%5Cmathrm%7BV%7D_%7B%5Cmathrm%7BJA%7D%7D%2B%5Cmathrm%7BM%7D_%7B%5Cmathrm%7BH%7D%7D%20%5Ctimes%20%5Cmathrm%7BV%7D_%7B%5Cmathrm%7BHA%7D%7D)
= 120 × (-2.5) + 140 × ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
= -300 + 140 × ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
We know that conservation of liner momentum,
Linear momentum before the collision = Linear momentum after the collision
80 = -300 + 140 × ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
80 + 300 = 140 × ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
380 = 140 × ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
380/140= ![V_{HA}](https://tex.z-dn.net/?f=V_%7BHA%7D)
= 2.71 m/s
2.71 m/s fast Hans is moving after the collision.
So,
GPE (graviational potential energy) = mass x g x height
GPE is depends on where zero height is defined. In this situation, we define h = 0 as the initial height.
![GPE = 75 \ kg*9.8 \ \frac{m}{s^2}*25 \ m](https://tex.z-dn.net/?f=GPE%20%3D%2075%20%5C%20kg%2A9.8%20%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%2A25%20%5C%20m)
![GPE = 18,375 \frac{kg*m^2}{s^2}](https://tex.z-dn.net/?f=GPE%20%3D%2018%2C375%20%5Cfrac%7Bkg%2Am%5E2%7D%7Bs%5E2%7D)
![GPE = 18,375 \ joules(J) \ or \ 18.375 \ kilojoules(kJ)](https://tex.z-dn.net/?f=GPE%20%3D%2018%2C375%20%5C%20joules%28J%29%20%5C%20or%20%5C%2018.375%20%5C%20kilojoules%28kJ%29)
The builder has gained 18.375 kJ of PE.
The astronaut would go the opposite direction due to Newton’s third law of -10N, -10N, -9N, -9N
Let me know if this helped you, please rank this was the brainlist answer if possible, thanks!
This actually means that the object which is emitting light spectrum is moving away from us.. how do you know that ? well.. it is clearly mentioned that it is a red shift so the wavelengths will stretched more . and thus the spectrum turns more reddish as it has higher wavelengths .. hence so called red shifts