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4 years ago

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A.The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the

deck to the street below.

1 answer:

Ainat [17]4 years ago

8 0

Answer:

8.68 seconds

Step-by-step explanation:

Given:

Height of the deck above the street, s = 370 m

Since the condition is of free falling

thus,

initial speed, u = 0

Acceleration of the penny = acceleration due to gravity, g = 9.81 m/s²

Now,

from Newton's equation of motion, we have

$s=ut+\frac{1}{2}at^2$

here,

s is the distance

a is the acceleration

t is the time

on substituting the values, we get

$370=0\times t+\frac{1}{2}\times9.81\times t^2$

or

t² = 75.433

or

t = 8.68 seconds

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Step-by-step explanation:

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3 years ago

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3 years ago

A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

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⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

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4 years ago

A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom

steposvetlana [31]

We can calculate the volume of a glass shell of the jar by calculating the total volume of a jar and then subtract the volume of air that fits in the jar (the space bounded by the shell).
The total volume of the jar is:
$V_t=Bh=\pi h(r+a)^2$
Where h is the height of the jar, a is the thickness and r is the inner radius.
The volume of empty space, bounded by the jar, is:
$V_e=B(h-a)=\pi r^2(h-a)$
The volume of a jar shell is the difference between these two:
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When we plug in all the number we get:
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The volume of water jar would displace depends how far the jar would sink.
There two forces acting on the jar when you put in the water. The first one is gravity and it's pulling the jar down. The second force is the buoyancy the and this force pushes the jar upward. In order for that jar to be stable, these two forces must be the same.
The buoyancy is given with this formula:
$B=\rho gV_{disp}$
The volume of water that would be displaced by the jar can be expressed by this formula:
$V_{disp}=\pi h'(r+a)^2$
Where h' is the height of the jar that is submerged in the water.
So the buoyancy force is:
$B=\rho_w g\pi h'(r+a)^2$
This force must be equal to the force of gravity acting on the jar:
$F_g=B\\ m_jg=\rho_w g\pi h'(r+a)^2\\ m_j=\rho_w \pi h'(r+a)^2\\$
We solve for h':
$h'=\frac{m_j}{\rho_w \pi(r+a)^2}$
If we plug in the number we get:
$h'=2.24 $in$
Now we can calcuate the amount of water discplaced and its mas(keep in mind that we also converted density of water into lb/in^3):
$V_{disp}=\pi h'(r+a)^2=71.50${in}^3\\
m_v=\rho_w\cdot V_{disp}=2.58$lb$
We get the same mass as the mass of the jar, which makes perfect sense:
$m_jg=\rho_w V_{disp}g\\
m_j=m_{wdisp}$

4 0

4 years ago