Mathematics, 27.08.2019 01:30 corbin3582

Consider the expression $2 \pi \sqrt{\frac{l}{g}}$ .
where ℓ is length and g is gravitational acceleration in units of length divided by time squared.
evaluate its units.
1. s²
2. $(\frac{s}{m})^2$
3. $(\frac{m}{s})^2$
4. $\frac{m}{s}$
5. s
6. m²
7. m
8. $\frac{s}{m}$

Answers: 3

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Answer from: payshencec21

Step-by-step explanation:

lets start from the expression $2\pi \sqrt{\frac{l}{g} }$ , first remember that $2\pi$ is a constant with no units, so we do not need to consider it for this problem, so lets just think about $\frac{l}{g}$

Next lets replace the units, l is the length which is represented in metters by international units system

g is the gravitational constants, so the units are lengt divided by time squared, since time is in seconds we have $\frac{m}{s^{2} }$

so pluging that into our formula we have $\sqrt{\frac{m}{\frac{m}{s^{2} } } }$

Now see we are dividing by a fraction, remember that to divide by a fraction is the same as to multiply by the reciprocal fraction, so we just flip the fraction and we get $\sqrt{m*\frac{s^{2} }{m} }$

then if we perform the multiplication we have inside the radical we get $\sqrt{\frac{m*s^{2} }{m} }$

Then since we are multiplying and dividing by m, the m's just cancel and we have $\sqrt{s^{2} }$

Now remember that square and square root are inverse operations, so they cancel each other and we are left with just , which means seconds, so the answer would be option 5

hope that helps, good bye :)

Answer from: Quest

answer: l

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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Consider the expression [tex]2 \pi \sqrt{\frac{l}{g}}[/tex].
where ℓ is length and g is gravi...