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Physics help needed (It's actually more math but it's supposed to be physics)

If anyone can help me with the following 4 questions it's be greatly appreciated! ... as you can see i'm not the best at proportion questions!

making T the subject of :
r(2π/T)^2=GM/r^2 (update! I managed to solve this one!)

(I'm going to copy out the next questions because it'll be easier to understand then me paraphrasing it)

The number of widgets made in a factory each week is proportional to the number of workers and the number of hours each worker works. When the factory employed 25 staff, each working 35 hours/week, 65400 widgets were made each week.
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?

A watch is set to the correct time at noon on 1st January and put in a drawer.
When it is checked at noon on 1st February, it reads 11:51:51::20.
What time did it read at 6:00am on 24th January?

A cyclist’s journey to work takes them 32minutes at 19km/h.
a)How long would it take at 15km/h?
b)How fast would they have to go to reduce the time to 25minutes?
(edited 5 years ago)
Original post by lcrabt21
If anyone can help me with the following 4 questions it's be greatly appreciated! ... as you can see i'm not the best at proportion questions!

making T the subject of :
r(2π/T)^2=GM/r^2

(I'm going to copy out the next questions because it'll be easier to understand then me paraphrasing it)

The number of widgets made in a factory each week is proportional to the number of workers and the number of hours each worker works. When the factory employed 25 staff, each working 35 hours/week, 65400 widgets were made each week.
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?

A watch is set to the correct time at noon on 1st January and put in a drawer.
When it is checked at noon on 1st February, it reads 11:51:20.
What time did it read at 6:00am on 24th January?

A cyclist’s journey to work takes them 32minutes at 19km/h.
a)How long would it take at 15km/h?
b)How fast would they have to go to reduce the time to 25minutes?


What have you tried so far in every single question?
Reply 2
Original post by dvx
What have you tried so far in every single question?


These are just a couple of questions I have tried to attempt and failed at.

The first one I followed some steps and managed to get T=4r^3π/GM the online website I am using to answer the questions said it was incorrect.

The second one I used the rule of Three calculators but got a different answer every time and they were all wrong so I think I'm looking at the question wrong there.

The third I managed to get 05:38:41 but it said I was wrong (initially I put it in as 11:38:41 and it said I had a problem with significant figures which confused me a little because I realised that it was supposed to be 05 and not 11)

The final one I started working out but I kept loosing where I was in my working.

I'm sure there are easier methods from the ones I was using and that's why I have reached out for help
Reply 3
Original post by lcrabt21
These are just a couple of questions I have tried to attempt and failed at.

The first one I followed some steps and managed to get T=4r^3π/GM the online website I am using to answer the questions said it was incorrect.

The second one I used the rule of Three calculators but got a different answer every time and they were all wrong so I think I'm looking at the question wrong there.

The third I managed to get 05:38:41 but it said I was wrong (initially I put it in as 11:38:41 and it said I had a problem with significant figures which confused me a little because I realised that it was supposed to be 05 and not 11)

The final one I started working out but I kept loosing where I was in my working.

I'm sure there are easier methods from the ones I was using and that's why I have reached out for help

Quick update! I managed to solve the first question but I am still stuck on the rest :/
Original post by lcrabt21
The number of widgets made in a factory each week is proportional to the number of workers and the number of hours each worker works. When the factory employed 25 staff, each working 35 hours/week, 65400 widgets were made each week.
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?


number of widgets in a week = k x w x t

where k is the constant of proportionality, w is the number of workers and t is the number of hours each worker works each week.

You can find the constant k by substituting the values from the first scenario into the equation. Then find the number of widgets made in the second week by substituting the value of k and the values from the second scenario into the equation.
Original post by lcrabt21
A cyclist’s journey to work takes them 32minutes at 19km/h.
a)How long would it take at 15km/h?
b)How fast would they have to go to reduce the time to 25minutes?


Speed = distance / time

a) Convert the minutes into hours and then find the total distance of the cyclists journey (speed = distance x time). Then find the time (time = distance / speed).

b) Convert 25 minutes into hours and then find the speed (speed = distance / time)
Reply 6
Original post by alevelphysicist
number of widgets in a week = k x w x t

where k is the constant of proportionality, w is the number of workers and t is the number of hours each worker works each week.

You can find the constant k by substituting the values from the first scenario into the equation. Then find the number of widgets made in the second week by substituting the value of k and the values from the second scenario into the equation.


Ok so I did 65'400 35+25 (=60)
so 65'400 60
65'400 divided by 60 = 1090
40+30 = 70
1090 x 70 = 76300
I also attempted at doing 35.625/15 which equals 2.375 x 60 which gives 142.5
It came back as wrong on both occasions, could you explain where I went wrong in my working out please? Thank you!!!
(edited 5 years ago)
Reply 7
Original post by alevelphysicist
Speed = distance / time

a) Convert the minutes into hours and then find the total distance of the cyclists journey (speed = distance x time). Then find the time (time = distance / speed).

b) Convert 25 minutes into hours and then find the speed (speed = distance / time)


I reattempted A but again got the wrong answer so could you please help me find out where I went wrong?
I did 32 divided by 60 which gives 0.53 recurring
then I did 19/5.3 recurring to give 35.625
after that I did 15/35.625 (speed/distance) which gave 0.42... which I converted back to minutes to give around 25 minutes, but of course that is wrong and I do not know how I have gone wrong :frown:
Original post by lcrabt21
Ok so I did 65'400 35+25 (=60)
so 65'400 60
65'400 divided by 60 = 1090
40+30 = 70
1090 x 70 = 76300
I also attempted at doing 35.625/15 which equals 2.375 x 60 which gives 142.5
It came back as wrong on both occasions, could you explain where I went wrong in my working out please? Thank you!!!


it’s 35 x 25 not 35 + 25
Original post by lcrabt21
I reattempted A but again got the wrong answer so could you please help me find out where I went wrong?
I did 32 divided by 60 which gives 0.53 recurring
then I did 19/5.3 recurring to give 35.625
after that I did 15/35.625 (speed/distance) which gave 0.42... which I converted back to minutes to give around 25 minutes, but of course that is wrong and I do not know how I have gone wrong :frown:


To find the distance you do 19 x 0.53333 (since distance = speed x time)
Reply 10
Original post by alevelphysicist
it’s 35 x 25 not 35 + 25


ahh I feel like an idiot now XD thank you so much for the help!

Is it the same sort of process for the question below?
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?
Reply 11
Original post by alevelphysicist
To find the distance you do 19 x 0.53333 (since distance = speed x time)


Ahhh that was such a silly mistake XD thank you again for the help!!!
Original post by lcrabt21
ahh I feel like an idiot now XD thank you so much for the help!

Is it the same sort of process for the question below?
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?


Yes, now you’ve got k you can calculate the number of workers needed now
Reply 13
Original post by lcrabt21
If anyone can help me with the following 4 questions it's be greatly appreciated! ... as you can see i'm not the best at proportion questions!

making T the subject of :
r(2π/T)^2=GM/r^2 (update! I managed to solve this one!)

(I'm going to copy out the next questions because it'll be easier to understand then me paraphrasing it)

The number of widgets made in a factory each week is proportional to the number of workers and the number of hours each worker works. When the factory employed 25 staff, each working 35 hours/week, 65400 widgets were made each week.
If we need 130000 widgets made each week, and the staff will work 42 hours/week, how many workers are needed?

A watch is set to the correct time at noon on 1st January and put in a drawer.
When it is checked at noon on 1st February, it reads 11:51:51::20.
What time did it read at 6:00am on 24th January?

A cyclist’s journey to work takes them 32minutes at 19km/h.
a)How long would it take at 15km/h?
b)How fast would they have to go to reduce the time to 25minutes?

how did u solve the Make T the subject of the following equation: r(T2π​)2=r2GM question?

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