Help please for Proportion questions

Two proportional questions needed help please

1.) the pressure of wat er P at any point below the surface of the sea varies as the depth of the point below the suface d. If the pressure is 200 newtons/cm² at a depth of 3m, calculate the pressure at a depth of 5m.

2.) The resistance to motion of a car is proportional to the suare of the speed of the car. If the resistance is 4000 newtons at a speed of 20 m/s, what is the resistance at a speed of 30 m/s?
And at what speed is the resistance 6250 newtons?

Reply 1

arktos

I'm assuming the pressure is directly proportional to the distance (d) from the surface?

a)Just say at 3m, pressure = 200
divide both sides by 3 , for 1m change in depth = 200/3 change in pressure
so 5m = (200/3)x5 = 1000/3 , about 333.33

b) 4000 at 20m/s
1m/s = 4000/20 = 200

for every 1m/s change in velocity there is a 200N change in resistive force.

at 30m/s :

force at 1 m/s x 30 = 200x30 = 6000N.

Any good?

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For every 1N change in resistance there is a velocity change associated with it of value:

1N = 20/4000 = 2/400 = 1/200

so at 6250 N , the velocity associated with it is , (1/200) x 6250 = 6250/200 = 31.25 m/s.

Reply 2

kevpang

no i dont get u can u explain to me once more please

Reply 3

Applying4Maths

I think you got 2) wrong, they weren't directly proportional, but the resistance is proportional to the square of the speed.

so 4000 = k 20^2 ==> 4000 = 400k ==> k=10 ==> F = 10 v^2

v=30: F = 10 x 30^2 = 10 x 900 = 9000N

F=6250: v = ?(F÷10) = ?(6250÷10) = ?625 = 25 m/s

Laura :wink:

Reply 4

kevpang

i m really confuse

can sumone one jsut tell me the answer for number 1 and 2 please

Reply 5

Esquire

if a is proportional to b then a=kb where k is a constant
if a is inversely proportional to b then a=k/b where k is a constant
if a is proportional to the square of b then a=kb^2 where k is a constant
if a is inversely proportional to the square of b then a=k/b^2 where k is a constant
you get the idea... proportion questions are all about applying these sorts of rules, dead easy once you have had practice :biggrin:

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the answer to 1) is 333.33 N/cm^3 and the answer to 2) is 25m/s

Reply 6

kevpang

cheeers, thats more like it
DEAD EASY

Reply 7

Esquire

good to know :biggrin:

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The only tricky part is the semantics question one says "(the pressure) varies as the depth" this means if I double the pressure, the depth doubles. In other words it is directly proportional. :biggrin:

Reply 8

arktos

sorry, didnt see that square speed bit.