Answer:
Explanation:
As we know that the ball is projected upwards so that it will reach to maximum height of 16 m
so we have
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
here we know that
![v_f = 0](https://tex.z-dn.net/?f=v_f%20%3D%200)
also we have
![a = -9.81 m/s^2](https://tex.z-dn.net/?f=a%20%3D%20-9.81%20m%2Fs%5E2)
so we have
![0 - v_i^2 = 2(-9.81)(16)](https://tex.z-dn.net/?f=0%20-%20v_i%5E2%20%3D%202%28-9.81%29%2816%29)
![v_i = 17.72 m/s](https://tex.z-dn.net/?f=v_i%20%3D%2017.72%20m%2Fs)
Now we need to find the height where its speed becomes half of initial value
so we have
![v_f = 0.5 v_i](https://tex.z-dn.net/?f=v_f%20%3D%200.5%20v_i)
now we have
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
![(0.5v_i)^2 - v_i^2 = 2(-9.81)h](https://tex.z-dn.net/?f=%280.5v_i%29%5E2%20-%20v_i%5E2%20%3D%202%28-9.81%29h)
![-0.75v_i^2 = -19.62 h](https://tex.z-dn.net/?f=-0.75v_i%5E2%20%3D%20-19.62%20h)
![0.75(17.72)^2 = 19.62 h](https://tex.z-dn.net/?f=0.75%2817.72%29%5E2%20%3D%2019.62%20h)
![h = 12 m](https://tex.z-dn.net/?f=h%20%3D%2012%20m)
Answer:
The objects must be different temperatures.
Explanation:
For heat to flow between two objects, heat must be flowing between them. The thermal gradient allows for the flow of heat. Heat is a form of energy that is dissipated from one place to another based on temperature difference.
Temperature is the degree of hotness or coldness of body. It is power by heat energy between two bodies.
Heat generally flows from a body at high temperature to one at low temperature. When thermal equilibrium is established and both bodies have the same temperature, heat will stop to flow.
Answer:
a) ![t=2s](https://tex.z-dn.net/?f=t%3D2s)
b) ![h_{max}=1024ft](https://tex.z-dn.net/?f=h_%7Bmax%7D%3D1024ft)
c) ![v_{y}=-256ft/s](https://tex.z-dn.net/?f=v_%7By%7D%3D-256ft%2Fs)
Explanation:
From the exercise we know the initial velocity of the projectile and its initial height
![v_{y}=64ft/s\\h_{o}=960ft\\g=-32ft/s^2](https://tex.z-dn.net/?f=v_%7By%7D%3D64ft%2Fs%5C%5Ch_%7Bo%7D%3D960ft%5C%5Cg%3D-32ft%2Fs%5E2)
To find what time does it take to reach maximum height we need to find how high will it go
b) We can calculate its initial height using the following formula
Knowing that its velocity is zero at its maximum height
![v_{y}^{2}=v_{o}^{2}+2g(y-y_{o})](https://tex.z-dn.net/?f=v_%7By%7D%5E%7B2%7D%3Dv_%7Bo%7D%5E%7B2%7D%2B2g%28y-y_%7Bo%7D%29)
![0=(64ft/s)^2-2(32ft/s^2)(y-960ft)](https://tex.z-dn.net/?f=0%3D%2864ft%2Fs%29%5E2-2%2832ft%2Fs%5E2%29%28y-960ft%29)
![y=\frac{-(64ft/s)^2-2(32ft/s^2)(960ft)}{-2(32ft/s^2)}=1024ft](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%2864ft%2Fs%29%5E2-2%2832ft%2Fs%5E2%29%28960ft%29%7D%7B-2%2832ft%2Fs%5E2%29%7D%3D1024ft)
So, the projectile goes 1024 ft high
a) From the equation of height we calculate how long does it take to reach maximum point
![h=-16t^2+64t+960](https://tex.z-dn.net/?f=h%3D-16t%5E2%2B64t%2B960)
![1024=-16t^2+64t+960](https://tex.z-dn.net/?f=1024%3D-16t%5E2%2B64t%2B960)
![0=-16t^2+64t-64](https://tex.z-dn.net/?f=0%3D-16t%5E2%2B64t-64)
Solving the quadratic equation
![t=\frac{-b±\sqrt{b^{2}-4ac}}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D)
![a=-16\\b=64\\c=-64](https://tex.z-dn.net/?f=a%3D-16%5C%5Cb%3D64%5C%5Cc%3D-64)
![t=2s](https://tex.z-dn.net/?f=t%3D2s)
So, the projectile reach maximum point at t=2s
c) We can calculate the final velocity by using the following formula:
![v_{y}^{2}=v_{o}^{2}+2g(y-y_{o})](https://tex.z-dn.net/?f=v_%7By%7D%5E%7B2%7D%3Dv_%7Bo%7D%5E%7B2%7D%2B2g%28y-y_%7Bo%7D%29)
![v_{y}=±\sqrt{(64ft/s)^{2}-2(32ft/s^2)(-960ft)}=±256ft/s](https://tex.z-dn.net/?f=v_%7By%7D%3D%C2%B1%5Csqrt%7B%2864ft%2Fs%29%5E%7B2%7D-2%2832ft%2Fs%5E2%29%28-960ft%29%7D%3D%C2%B1256ft%2Fs)
Since the projectile is going down the velocity at the instant it reaches the ground is:
![v=-256ft/s](https://tex.z-dn.net/?f=v%3D-256ft%2Fs)
Answer:
I'm pretty sure it's 37.5 joules of energy
Explanation:
hope this helps!
Elements that give up electrons easily are called <u>metals.</u>
hope this helps!