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enot [183]
3 years ago
8

A ball is thrown in the air with a vertical velocity of 12 m/s.

Physics
2 answers:
melamori03 [73]3 years ago
4 0
The answer to the question is gonna be A
Ipatiy [6.2K]3 years ago
4 0

Answer:

a) 1.22 s

b) 6 m/s

c) 7.35 m

Explanation:

Given:

v₀ = 12 m/s

a = -9.8 m/s²

a) Find t when v = 0 m/s.

v = at + v₀

(0 m/s) = (-9.8 m/s²) t + (12 m/s)

t = 1.22 s

b) v_avg = ½ (v₀ + v)

v_avg = ½ (12 m/s + 0 m/s)

v_avg = 6 m/s

c) Find Δx.

v² = v₀² + 2aΔx

(0 m/s)² = (12 m/s)² + 2 (-9.8 m/s²) Δx

Δx = 7.35 m

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A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at
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Answer:

Y=(\dfrac{3}{16}+t \dfrac{3}{8})e^{-2t}-\dfrac{3}{16}cos 4t

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Given that m= 1 slug and given that spring stretches by 2 feet so we can find the spring constant K

mg=k x

1 x 32= k x 2

K=16

And also give that damping force is 8 times the velocity so damping constant C=8.

We know that equation for spring mass system

my''+Cy'+Ky=F

Now by putting the values

1 y"+8 y'+ 16y=6 cos 4 t ----(1)

The general solution of equation Y=CF+IP

Lets assume that at steady state the equation of y will be

y(IP)=A cos 4t+ B sin 4t

To find the constant A and B we have to compare this equation with equation 1.

Now find y' and y" (by differentiate with respect to t)

y'= -4A sin 4t+4B cos 4t

y"=-16A cos 4t-16B sin 4t

Now put the values of y" , y' and y in equation 1

1 (-16A cos 4t-16B sin 4t)+8( -4A sin 4t+4B cos 4t)+16(A cos 4t+ B sin 4t)=6sin4 t

So by comparing the coefficient both sides

-16A+32B+16A=0  So B=0

-16 B-32 A+16B=6  So A=-3/16

y=-3/16 cos 4t

Now to find the CF  of differential equation 1

y"+8 y'+ 16y=6 cos 4 t

Homogeneous version of above equation

m^2+8m+16=0

So CF =(C_1+tC_2)e^{-2t}

So the general equation

Y=(C_1+tC_2)e^{-2t}-3/16 cos 4t

Given that t=0 Y=0 So

C_1=\dfrac{3}{16}

t=0 Y'=0 So

C_2 =\dfrac{3}{8}

Y=(\dfrac{3}{16}+t \dfrac{3}{8})e^{-2t}-\dfrac{3}{16}cos 4t

The above equation is the general equation for motion.

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Based on this, the order of MOST to LEAST ordered particle arrangement is solid - liquid- gas i.e. wood - water - neon gas.

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