Answer:
vf = 22.36[m/s]
Explanation:
First we must understand the data given in the problem:
m = mass = 800 [kg]
F = force = 20000[N]
dx = displacement = 10[m]
From newton's second we know that the sum of forces must be equal to the product of mass by acceleration.
![F = m*a\\20000 = 800*a\\a = 20000/800\\a = 25 [m/s^2]](https://tex.z-dn.net/?f=F%20%3D%20m%2Aa%5C%5C20000%20%3D%20800%2Aa%5C%5Ca%20%3D%2020000%2F800%5C%5Ca%20%3D%2025%20%5Bm%2Fs%5E2%5D)
With the calculated acceleration, we can use the kinematics equations.
![v_{f} ^{2} =v_{o} ^{2}+2*a*dx\\ v_{o} = initial velocity = 0\\a = acceleration = 25[m/s^2]\\dx= displacement = 10[m]\\](https://tex.z-dn.net/?f=v_%7Bf%7D%20%5E%7B2%7D%20%3Dv_%7Bo%7D%20%5E%7B2%7D%2B2%2Aa%2Adx%5C%5C%20v_%7Bo%7D%20%3D%20initial%20velocity%20%3D%200%5C%5Ca%20%3D%20acceleration%20%3D%2025%5Bm%2Fs%5E2%5D%5C%5Cdx%3D%20displacement%20%3D%2010%5Bm%5D%5C%5C)
The key to using this equation is to clarify that the initial velocity is zero since the body is at rest, otherwise the initial velocity would be an initial data.
![v_{f} =\sqrt{2*25*10} \\v_{f} =22.36[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%20%3D%5Csqrt%7B2%2A25%2A10%7D%20%5C%5Cv_%7Bf%7D%20%3D22.36%5Bm%2Fs%5D)
Another way of solving this problem is by means of the definition of work and kinetic energy, where work is defined as the product of the force by the distance.
W =F*d
W = 20000*10
W = 200000[J]
Kinetic energy is equal to work, therefore the value calculated above is equal to:
![E_{k}=W =0.5*m*v_{f}^{2} \\200000=0.5*800*v_{f}^{2}\\v_{f}=\sqrt{\frac{200000}{0.5*800} } \\v_{f}=22.36[m/s]](https://tex.z-dn.net/?f=E_%7Bk%7D%3DW%20%3D0.5%2Am%2Av_%7Bf%7D%5E%7B2%7D%20%5C%5C200000%3D0.5%2A800%2Av_%7Bf%7D%5E%7B2%7D%5C%5Cv_%7Bf%7D%3D%5Csqrt%7B%5Cfrac%7B200000%7D%7B0.5%2A800%7D%20%7D%20%5C%5Cv_%7Bf%7D%3D22.36%5Bm%2Fs%5D)
The Doppler effect helps aid in forecasting the velocity of objects.
This could include precipitation in the atmosphere!
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Answer:
d = ( -0.3 , 0.7 ) miles
Explanation:
The complete question is as follows:
" Take the north direction as the positive y direction and east as positive x. The origin is still where the student starts biking. Let d⃗ N be the displacement vector corresponding to the first leg of the student's trip. Express d⃗ N in component form.
Express your answer as two numbers separated by a comma (e.g., 1.0,2.0). By convention, the x component is written first.
A student bikes to school by traveling first dN = 0.800 miles north, then dW = 0.300 miles west, and finally dS = 0.100 miles south. "
Solution:
- The displacement vector d N is vector sum of all journeys. We will express +x as +i and +y as +j. Then displacement vector is given by:
d = dN + dW + dS
d = 0.8 j - 0.3 i - 0.1 j
d = - 0.3 i + 0.7 j
- The displacement vector d in component form is d = ( -0.3 , 0.7 ) miles