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ollegr [7]
3 years ago
14

A solid steel ball is thrown directly downward, with an initial speed of 7.95 m/s, from the top of a building at a height of 29.

8 m. How much time (in s) does it take before striking the ground?
Physics
1 answer:
Anika [276]3 years ago
5 0

Answer:

1.78 s

Explanation:

Initial speed of the ball = u = 7.95 m/s and is vertically downwards.

Acceleration due to gravity = g = 9.8 m/s/s , vertically downwards.

Height of the building  h = 29.8 m (traversed downwards by the steel ball).

h = u t + 1/2 g t²

29.8 = 7.95 t + 0.5 (9.8) t²

⇒ 4.9 t² +7.95 t - 29.8 = 0

Using the quadratic formula , solve for t.

t= = \frac{-b\pm \sqrt{b^2-4\times a \times c}}{2\times a}

t = \frac{-7.95 \pm \sqrt{7.95^2-4\times 4.9 \times (-29.8)}}{2\times 9.8} = 1.78 s, -3.4 s

Since time does not have a negative value, time taken by the stone to reach the ground = t = 1.78 s

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Answer:

a) v = c \cdot 0.04 = 1.2\cdot 10^{7} m/s

b) v = c \cdot 0.71 = 2.1\cdot 10^{8} m/s

c) v = c \cdot 0.994 = 2.97\cdot 10^{8} m/s

d) v = c \cdot 0.999 = 2.997\cdot 10^{8} m/s

e) v = c \cdot 0.9999 = 2.999\cdot 10^{8} m/s

Explanation:

At that energies, the speed of proton is in the relativistic theory field, so we need to use the relativistic kinetic energy equation.

KE=mc^{2}(\gamma -1) = mc^{2}(\frac{1}{\sqrt{1-\beta^{2}}} -1)           (1)

Here β = v/c, when v is the speed of the particle and c is the speed of light in vacuum.

Let's solve (1) for β.

\beta = \sqrt{1-\frac{1}{\left (\frac{KE}{mc^{2}}+1 \right )^{2}}}

We can write the mass of a proton in MeV/c².

m_{p}=938.28 MeV/c^{2}

Now we can calculate the speed in each stage.

a) Cockcroft-Walton (750 keV)

\beta = \sqrt{1-\frac{1}{\left (\frac{0.75 MeV}{938.28 MeV}+1 \right )^{2}}}

\beta = 0.04

v = c \cdot 0.04 = 1.2\cdot 10^{7} m/s

b) Linac (400 MeV)

\beta = \sqrt{1-\frac{1}{\left (\frac{400 MeV}{938.28 MeV}+1 \right )^{2}}}

\beta = 0.71

v = c \cdot 0.71 = 2.1\cdot 10^{8} m/s

c) Booster (8 GeV)

\beta = \sqrt{1-\frac{1}{\left (\frac{8000 MeV}{938.28 MeV}+1 \right )^{2}}}

\beta = 0.994

v = c \cdot 0.994 = 2.97\cdot 10^{8} m/s

d) Main ring or injector (150 Gev)

\beta = \sqrt{1-\frac{1}{\left (\frac{150000 MeV}{938.28 MeV}+1 \right )^{2}}}

\beta = 0.999

v = c \cdot 0.999 = 2.997\cdot 10^{8} m/s

e) Tevatron (1 TeV)

\beta = \sqrt{1-\frac{1}{\left (\frac{1000000 MeV}{938.28 MeV}+1 \right )^{2}}}

\beta = 0.9999

v = c \cdot 0.9999 = 2.999\cdot 10^{8} m/s

Have a nice day!

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4 years ago
If someone is whispering, but you cant hear them, how do you fix that problem?
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The answer is C
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An arrow is shot vertically upward at a rate of 250ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in
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Answer:

The arrow is at a height of 500 feet at time t = 2.35 seconds.

Explanation:

It is given that,

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The projectile formula is given by :

h=-16t^2+v_ot

We need to find the time(s), in seconds, the arrow is at a height of 500 ft. So,

-16t^2+250t=500

On solving the above quadratic equation, we get the value of t as, t = 2.35 seconds

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3 years ago
A 5 kg projectile is fired at an angle of 25o above the horizontal. Its initial velocity is 200 m/s and just before it hits the
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Answer:

The change in the mechanical energy of the projectile is 43,750 J

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final velocity of the projectile, v = 150 m/s

The change in mechanical energy is calculated from the principle of conservation of energy;

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ΔK.E = ¹/₂m(u² - v²)

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ΔK.E =  43,750 J

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3 years ago
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