1. C
2. A
3. E
4. D
5. B
6. F
i might have 2 and 6 mixed up, not completely sure tho
Here’s a good photo to reference when converting in the metric system.
Each time you move down a step you move the decimal to the right, each time you move up a step you move the decimal to the left.
We are going from 1.2 kg or kilograms, which is at the very top left of the ladder. To get to mg or milligrams, we would have to make six jumps, so we’d move the decimal over six times.
1.2 > 12. > 120. > 1200. > 12000. > 120000. > 1200000.
So our final answer would be 1,200,000mg.
Answer:
a) ![v=7.32m/s](https://tex.z-dn.net/?f=v%3D7.32m%2Fs)
b)
º
c) ![ΔK=-1094.62J](https://tex.z-dn.net/?f=%CE%94K%3D-1094.62J)
Explanation:
From the exercise we know that the collision between Daniel and Rebecca is elastic which means they do not stick together
So, If we analyze the collision we got
![p_{1x}=p_{2x}](https://tex.z-dn.net/?f=p_%7B1x%7D%3Dp_%7B2x%7D)
To simplify the problem, lets name D for Daniel and R for Rebecca
a) ![p_{D1x}+p_{R1x}=p_{D2x}+p_{R2x}](https://tex.z-dn.net/?f=p_%7BD1x%7D%2Bp_%7BR1x%7D%3Dp_%7BD2x%7D%2Bp_%7BR2x%7D)
Since Daniel's initial velocity is 0
![m_{R}v_{Rx}=m_{D}v_{D2x}+m_{R}v_{R2x}](https://tex.z-dn.net/?f=m_%7BR%7Dv_%7BRx%7D%3Dm_%7BD%7Dv_%7BD2x%7D%2Bm_%7BR%7Dv_%7BR2x%7D)
![v_{D2x}=\frac{m_{R}*v_{R1x}-m_{R}*v_{R2x}}{m_{D}}](https://tex.z-dn.net/?f=v_%7BD2x%7D%3D%5Cfrac%7Bm_%7BR%7D%2Av_%7BR1x%7D-m_%7BR%7D%2Av_%7BR2x%7D%7D%7Bm_%7BD%7D%7D)
![v_{D2x}=\frac{(45kg)(14m/s)-(45kg)(8cos(55.1)m/s)}{(70kg)}=6m/s](https://tex.z-dn.net/?f=v_%7BD2x%7D%3D%5Cfrac%7B%2845kg%29%2814m%2Fs%29-%2845kg%29%288cos%2855.1%29m%2Fs%29%7D%7B%2870kg%29%7D%3D6m%2Fs)
Now, lets analyze the movement in the vertical direction
![p_{1y}=p_{2y}](https://tex.z-dn.net/?f=p_%7B1y%7D%3Dp_%7B2y%7D)
Since ![p_{1y}=0](https://tex.z-dn.net/?f=p_%7B1y%7D%3D0)
![0=m_{D}v_{D2y}+m_{R}v_{R2y}](https://tex.z-dn.net/?f=0%3Dm_%7BD%7Dv_%7BD2y%7D%2Bm_%7BR%7Dv_%7BR2y%7D)
![v_{D2y}=-\frac{m_{R}v_{2Ry}}{m_{D}}=-\frac{(45kg)(8sin(55.1)m/s)}{(70kg)}=-4.21m/s](https://tex.z-dn.net/?f=v_%7BD2y%7D%3D-%5Cfrac%7Bm_%7BR%7Dv_%7B2Ry%7D%7D%7Bm_%7BD%7D%7D%3D-%5Cfrac%7B%2845kg%29%288sin%2855.1%29m%2Fs%29%7D%7B%2870kg%29%7D%3D-4.21m%2Fs)
Now, we can find the magnitude of Daniel's velocity after de collision
![v_{D}=\sqrt{(6m/s)^2+(-4.21m/s)^2}=7.32m/s](https://tex.z-dn.net/?f=v_%7BD%7D%3D%5Csqrt%7B%286m%2Fs%29%5E2%2B%28-4.21m%2Fs%29%5E2%7D%3D7.32m%2Fs)
b) To know whats the direction of Daniel's velocity we need to solve the arctan of the angle
º
c) The change in the total kinetic energy is:
ΔK=![K_{2}-K_{1}](https://tex.z-dn.net/?f=K_%7B2%7D-K_%7B1%7D)
ΔK=![\frac{1}{2}[(45kg)(8m/s)^2+(70kg)(7.32m/s)^2-(45kg)(14m/s)^2]=-1094.62J](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%2845kg%29%288m%2Fs%29%5E2%2B%2870kg%29%287.32m%2Fs%29%5E2-%2845kg%29%2814m%2Fs%29%5E2%5D%3D-1094.62J)
That means that the kinetic energy decreases
Too much skepticism will lead one to doubt everything while too little will lead to gullibility.
The change in gravitational potential energy is A) 15.68 J
Explanation:
The gravitational potential energy of an object is the energy possessed by the object due to its position in the gravitational field.
The change in gravitational potential energy of an object is given by the equation:
![\Delta U = mg\Delta h](https://tex.z-dn.net/?f=%5CDelta%20U%20%3D%20mg%5CDelta%20h)
where
m is the mass of the object
is the acceleration due to gravity
is the change in height of the object
In this problem, we have
m = 2 kg is the mass of the frame
is the change in height
Substituting, we find:
![\Delta U = (2)(9.8)(0.8)=15.68 J](https://tex.z-dn.net/?f=%5CDelta%20U%20%3D%20%282%29%289.8%29%280.8%29%3D15.68%20J)
Learn more about potential energy:
brainly.com/question/1198647
brainly.com/question/10770261
#LearnwithBrainly