Answer:
The heat energy required is, E = 2200 J
Explanation:
Given,
The mass of paraffin, m = 2 Kg
The energy required to raise the temperature of the paraffin by 200° C = 44000 J
Then the heat energy required to raise the temperature of the paraffin by 10° C is given by,
Since 44000 J raises temperature by 200° C, then
E = 44000 J / 20
= 2200 J
Hence, the energy required to raise the temperature of the paraffin by 10° C is, E = 2200 J
Answer:
Explanation:
Distance and direction of an object's change in position from a starting point. Displacement. 3. Jermaine runs exactly 2 laps around a 400 meter track. What is the displacement? 0 ... David walks 3 km north, and then turns east and walks 4 km. ... A person walks 50 meters directly north, stops, and then travels 32 meters
Answer:
![t = 1.82](https://tex.z-dn.net/?f=t%20%3D%201.82)
Explanation:
Given
-- initial velocity
--- height
Required
Determine the time to hit the ground
This will be solved using the following motion equation.
![s = ut + \frac{1}{2}gt^2](https://tex.z-dn.net/?f=s%20%3D%20ut%20%2B%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
Where
![g = 9,8m/s^2](https://tex.z-dn.net/?f=g%20%3D%209%2C8m%2Fs%5E2)
So, we have:
![30.2 = 7.70t + \frac{1}{2} * 9.8 * t^2](https://tex.z-dn.net/?f=30.2%20%3D%207.70t%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%2A%209.8%20%2A%20t%5E2)
![30.2 = 7.70t + 4.9 * t^2](https://tex.z-dn.net/?f=30.2%20%3D%207.70t%20%2B%204.9%20%2A%20t%5E2)
Subtract 30.2 from both sides
![30.2 -30.2 = 7.70t + 4.9 * t^2 - 30.2](https://tex.z-dn.net/?f=30.2%20-30.2%20%20%3D%207.70t%20%2B%204.9%20%2A%20t%5E2%20-%2030.2)
![0 = 7.70t + 4.9 * t^2 - 30.2](https://tex.z-dn.net/?f=0%20%20%3D%207.70t%20%2B%204.9%20%2A%20t%5E2%20-%2030.2)
![0 = 7.70t + 4.9t^2 - 30.2](https://tex.z-dn.net/?f=0%20%20%3D%207.70t%20%2B%204.9t%5E2%20-%2030.2)
![7.70t + 4.9t^2 - 30.2 = 0](https://tex.z-dn.net/?f=7.70t%20%2B%204.9t%5E2%20-%2030.2%20%20%3D%200)
![4.9t^2 + 7.70t - 30.2 = 0](https://tex.z-dn.net/?f=4.9t%5E2%20%2B%207.70t%20-%2030.2%20%20%3D%200)
Solve using quadratic formula:
![t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
Where
![a = 4.9;\ b = 7.70;\ c = -30.2](https://tex.z-dn.net/?f=a%20%3D%204.9%3B%5C%20b%20%3D%207.70%3B%5C%20c%20%3D%20-30.2)
![t = \frac{-7.70\±\sqrt{7.70^2 - 4*4.9*-30.2}}{2*4.9}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-7.70%5C%C2%B1%5Csqrt%7B7.70%5E2%20-%204%2A4.9%2A-30.2%7D%7D%7B2%2A4.9%7D)
![t = \frac{-7.70\±\sqrt{651.21}}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-7.70%5C%C2%B1%5Csqrt%7B651.21%7D%7D%7B9.8%7D)
![t = \frac{-7.70\±25.52}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-7.70%5C%C2%B125.52%7D%7B9.8%7D)
Split the expression
or ![t = \frac{-7.70-25.52}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-7.70-25.52%7D%7B9.8%7D)
or ![t = -\frac{33.22}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B33.22%7D%7B9.8%7D)
Time can't be negative; So, we have:
![t = \frac{17.82}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B17.82%7D%7B9.8%7D)
![t = 1.82](https://tex.z-dn.net/?f=t%20%3D%201.82)
Hence, the time to hit the ground is 1.82 seconds
<h2>
The asteroid is 4.11 x 10¹¹ m far from Sun</h2>
Explanation:
We have gravitational force
![F=\frac{GMm}{r^2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BGMm%7D%7Br%5E2%7D)
Where G = 6.67 x 10⁻¹¹ N m²/kg²
M = Mass of body 1
M = Mass of body 2
r = Distance between them
Here we have
M = Mass of Sun = 1.99×10³⁰ kg
m = Mass of asteroid = 4.00×10¹⁶ kg
F = 3.14×10¹³ N
Substituting
![F=\frac{GMm}{r^2}\\\\3.14\times 10^{13}=\frac{6.67\times 10^{-11}\times 1.99\times 10^{30}\times 4\times 10^{16}}{r^2}\\\\r=4.11\times 10^{11}m](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BGMm%7D%7Br%5E2%7D%5C%5C%5C%5C3.14%5Ctimes%2010%5E%7B13%7D%3D%5Cfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%201.99%5Ctimes%2010%5E%7B30%7D%5Ctimes%204%5Ctimes%2010%5E%7B16%7D%7D%7Br%5E2%7D%5C%5C%5C%5Cr%3D4.11%5Ctimes%2010%5E%7B11%7Dm)
The asteroid is 4.11 x 10¹¹ m far from Sun