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3 years ago

7

A stone dropped from the top of a building reaches the ground with a velocity of 49ms¹. If the acceleration due to gravity is 9.

8ms², calculate the time for which the stone is falling freely. [Answer: 5s]

1 answer:

bezimeni [28]3 years ago

6 0

Explanation:

Given:

v₀ = 0 m/s

v = 49 m/s

a = 9.8 m/s²

Find: t

v = at + v₀

49 m/s = (9.8 m/s²) t + 0 m/s

t = 5 s

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Answer:23hz

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3 years ago

How much must a woman weigh ( force) if the pressure she exerts while standing on one foot has an area of 0.6m squared exerts a

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Answer:

W = 9.6 N

Explanation:

Given that,

Area on 1 foot, A = 0.6 m²

Pressure, P = 16 Pa

The pressure is given by force acting per unit area. So,

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So, the required weight is 9.6 N.

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3 years ago

A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

dolphi86 [110]

To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.

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Here,

M = Mass

R = Radius of the hoop

The precession frequency is given as

$\Omega = \frac{Mgd}{I\omega}$

Here,

M = Mass

g= Acceleration due to gravity

d = Distance of center of mass from pivot

I = Moment of inertia

$\omega$ = Angular velocity

Replacing the value for moment of inertia

$\Omega= \frac{MgR}{MR^2 \omega}$

$\Omega = \frac{g}{R\omega}$

The value for our angular velocity is not in SI, then

$\omega = 1000rpm (\frac{2\pi rad}{1 rev})(\frac{1min}{60s})$

$\omega = 104.7rad/s$

Replacing our values we have that

$\Omega = \frac{9.8m/s^2}{(8*10^{-2}m)(104.7rad)}$

$\Omega = 1.17rad/s$

The precession frequency is

$\Omega = \frac{2\pi rad}{T}$

$T = \frac{2\pi rad}{\Omega}$

$T = \frac{2\pi}{1.17}$

$T = 5.4 s$

Therefore the precession period is 5.4s

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3 years ago

Find the mass of an object if a 40 N of force causes the object to accelerate at 5.5 m/s/s

Murrr4er [49]

Answer:

<h3>The answer is 8 kg</h3>

Explanation:

The mass of the object can be found by using the formula

$m = \frac{f}{a} \\$

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From the question we have

$m = \frac{40}{5} \\$

We have the final answer as

<h3>8 kg</h3>

Hope this helps you

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3 years ago

a gym consists of a rectangular region with a semi-circle on each end. if the perimeter of the room is to be a 200 m running tra

Nikolay [14]

The dimensions of the rectangle are:

l = 50 m

b = $100/\pi$ m

<h3>What is a perimeter in math?</h3>

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides.

<h3>How do we find a perimeter of a rectangle?</h3>

The perimeter of a rectangle,denoted by P is given by the formula, P=2l+2b, where l is the length and b is the breadth of the rectangle.

<h3>Given:</h3>

As per the question:

Perimeter of the room is given as P = 200 m

The region is rectangular having a semicircle at each end.

Now,

Let 'l' be the length of the rectangle, 'b' be its breadth and 'r' be the radius of the semi-circle at each end.

Then, Area of the given rectangle, A = lb

Perimeter of the room, P is = $\pi r+l+\pi r+l=2\pi r+2l=\pi b+2l$

Therefore, $\pi b+2l=200$

$b=(200-2l)/\pi$

Now,

Area, A = $l(200-2l)/\pi=(200l-2l^{2} )/\pi$

Now, differentiate A w.r.t l:

Again differentiating w.r.t 'l', we get:

$d^{2} A/dl^{2} =-4l/\pi$ < 0

Thus we get maximum are when $dA/dl=0$

Therefore,

$(200-4l)/\pi=0$

l = 50 m

Now, from

$\pi b+2l=200$

$\pi b=200-2*50$

$b=100/\pi$

$r=b/2=50/\pi$

To know more about area of a recatangle, visit the link

brainly.com/question/20693059

#SPJ4

4 0

1 year ago