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
Answer:
an ellipse with the Sun at one focus or D
Explanation:
Answer for edgenuity
Answer:
To calculate displacement, simply draw a vector from your starting point to your final position and solve for the length of this line. If your starting and ending position are the same, like your circular 5K route, then your displacement is 0. In physics, displacement is represented by Δs.
Explanation:
hope helps
The displacement of Itzel according to the question is 6.3 miles SW
Displacement is defined as the distance moved by a body in a specified direction
Find the diagram attached
From the diagram given, we can see that AB is the displacement
To get the length AB, we will have to use the Pythagoras theorem:
![AB^2=2^2+ 6^2\\AB^2 ^2=4+36\\AB^2=40\\AB=\sqrt{40}\\AB= 6.3 miles\\](https://tex.z-dn.net/?f=AB%5E2%3D2%5E2%2B%206%5E2%5C%5CAB%5E2%20%5E2%3D4%2B36%5C%5CAB%5E2%3D40%5C%5CAB%3D%5Csqrt%7B40%7D%5C%5CAB%3D%206.3%20miles%5C%5C)
From the diagram, we can also se that the direction of the displacement in the South West direction.
Hence the displacement of Itzel according to the question is 6.3 miles SW
Learn more here: brainly.com/question/19108075
Answer:
![T=9.42Nm](https://tex.z-dn.net/?f=T%3D9.42Nm)
Explanation:
From the question we are told that:
Radius ![r= 0.5 m](https://tex.z-dn.net/?f=r%3D%200.5%20m)
Current ![I= 3.0 A](https://tex.z-dn.net/?f=I%3D%203.0%20A)
Normal vector ![n=\frac{(2i - j +2k)}{3}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B%282i%20-%20j%20%2B2k%29%7D%7B3%7D)
Magnetic field ![B= (2i-6j) T](https://tex.z-dn.net/?f=B%3D%20%282i-6j%29%20T)
Generally the equation for Area is mathematically given by
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
![A=3.1415 *0.5^2](https://tex.z-dn.net/?f=A%3D3.1415%20%2A0.5%5E2)
![A=0.7853 m^2](https://tex.z-dn.net/?f=A%3D0.7853%20m%5E2)
Generally the equation for Torque is mathematically given by
![T=A(i'*B)](https://tex.z-dn.net/?f=T%3DA%28i%27%2AB%29)
Where
![i'*B= \begin{bmatrix}2&-1&2\\2&-6&0\end{bmatrix}](https://tex.z-dn.net/?f=i%27%2AB%3D%20%5Cbegin%7Bbmatrix%7D2%26-1%262%5C%5C2%26-6%260%5Cend%7Bbmatrix%7D)
![X\ component\ of\ i'*B= [(-1 * 0)-(2*-6)]](https://tex.z-dn.net/?f=X%5C%20component%5C%20of%5C%20i%27%2AB%3D%20%5B%28-1%20%2A%200%29-%282%2A-6%29%5D)
![X\ component\ of\ i'*B=12](https://tex.z-dn.net/?f=X%5C%20component%5C%20of%5C%20i%27%2AB%3D12)
Therefore
![T=0.7853*12](https://tex.z-dn.net/?f=T%3D0.7853%2A12)
![T=9.42Nm](https://tex.z-dn.net/?f=T%3D9.42Nm)