By using_______you can determine your exact position and altitude on earth?

You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen

Paladinen [302]

Answer:

(A)

$\displaystyle D^2-\left (\frac{2v_s^2}{g}+2t_tv_s \right )D+t_t^2v_s^2=0$

(B) D=54.71 m

Explanation:

Free Fall

When a particle is dropped in free air, it starts falling to the ground with an acceleration equal to the gravity. If one wanted to know the height of launching, it can indirectly be measured by the time it takes to reach the ground by the formula

$\displaystyle D=\frac{gt^2}{2}$

Solving for t

$\displaystyle t=\sqrt{\frac{2D}{g}}$

If we are taking into consideration the time we can hear the sound it makes when hitting the ground (or water in this case), we must also consider the speed of the sound for the time it takes to reach back our ears. That time can be computed from the basic equation for the speed

$\displaystyle t=\frac{D}{v_s}$

(A)

The total measured time is the sum of both times and it's given as $t_t=3.5\ seconds$

$\displaystyle t_t=\sqrt{\frac{2D}{g}}+\frac{D}{v_s}$

From this equation we'll manage to compute D

First, we isolate the square root

$\displaystyle \sqrt{\frac{2D}{g}}=t_t-\frac{D}{v_s}$

Let's square both sides

$\displaystyle \frac{2D}{g}=t_t^2-2t_t\frac{D}{v_s}+\frac{D^2}{v_s^2}$

Multiplying by $v_s^2$

$\displaystyle \frac{2Dv_s^2}{g}=t_t^2v_s^2-2t_tDv_s+D^2$

Rearranging and factoring

$\boxed{\displaystyle D^2-\left (\frac{2v_s^2}{g}+2t_tv_s\right )D+t_t^2v_s^2=0}$

Now, let's put in numbers:

$g=9.8\ m/s^2,\ v_s=345\ m/s,t_t=3.5\ sec$

$\displaystyle D^2-\left (\frac{2(345)^2}{9.8}+2(3.5)(345)\right )D+(12.25)345^2=0$

Computing all the coefficients:

$\displaystyle D^2-26,705.82D+1,458,056.25=0$

Solving for D, we have two possible solutions:

$D=54.71,\ D=26,651.11$

The second solution is called "extraneous", since it comes from squaring an equation, which can introduce non-valid (or external) solutions. It's impossible, given the conditions of the problem, that the well could be 26.5 km deep. So we'll keep the only solution as.

D=54.71 m

Let's prove our calculations by computing both times:

$\displaystyle t_1=\sqrt{\frac{2(54.71)}{9.8}}=3.34\ sec$

$\displaystyle t_2=\frac{54.71}{345}=0.16\ sec$

We can see their sum is 3.5 seconds, 3.34 of which were taken to reach the bottom of the well, and 0.16 sec took the sound to reach the top.

3 0

2 years ago

El valor más preciso de la masa de un electron es 9.11*10^-11kg ¿ Cuánto aumentaría la masa de un cuerpo que se carga con -1 c d

chubhunter [2.5K]

Answer:

$m = 569.375\times 10^{6}\,kg$

Explanation:

Un electrón tiene una carga negativa de $1.6\times 10^{-19}\,C$ y la masa total es igual al producto del número de electrones y esa carga unitaria. El número de electrones se obtiene al dividir la carga total por la carga unitaria. (An electron has a negative charge of $1.6\times 10^{-19}\,C$ and the total mass is equal to the product of the qunatity of electrons and such unit charge. The quantity of electrons is found by diving the total charge by the unit charge):

$m = \frac{Q}{q} \cdot m_{e}$

$m = \left(\frac{1\,C}{1.6\times 10^{-19}\,C} \right)\cdot (9.11\times 10^{-11}\,kg)$

$m = 569.375\times 10^{6}\,kg$

7 0

2 years ago

Two technicians are discussing torque wrenches. Technician A says that a torque wrench is capable of tightening a fastener with

USPshnik [31]

Djfigud ticks fjyigud dhy

7 0

2 years ago

What is the speed of gravity

mojhsa [17]

9.8m per seccond is the speed of gravity if you drop something like a ball from a tower

8 0

3 years ago

An element emits a spectrum that____________.a)is evenly spaced.b)is the same as all other elements.c)is unique to that element.

Fittoniya [83]

Answer:

c)is unique to that element

Explanation:

The spectrum emitted by a element shows the internal electronic structure of that element.We know that all element is having different internal electronic structure that is why all element emits different spectrum.And the spacing between the spectrum is uneven .

Therefore the answer will be option C.

c)is unique to that element

5 0

2 years ago