Expert: Paul Klarreich - 8/14/2011

Question
QUESTION: plz answer me in detail of these questions.
1.a stone is thrown vertically upward so that its distance bove the ground in t seconds is s is equal to 84t-5t2(sqare).find the times when the stone is at hight 62m above the ground.
2.a stone is thrown vertically upward with an initial speed of 56m/s.its hight h metres above the ground after t sec is given by the formula 56t-5t2(square is on t).after how many sec will the stone be 50 m above the ground.
a front wheelsof a vehicle are 50 cm greater in circumference than the back wheels.the back wheels make 3 revolutions more than the front wheels in a distance of 15 m .find the circumference of the front wheels.

ANSWER: Questioner:NADIA
Country:Punjab, Pakistan
Category:Advanced Math
Private:No
Subject:urgent

Question:

plz answer me in detail of these questions.
1.a stone is thrown vertically upward so that its distance bove the ground in t seconds is s is equal to 84t-5t2(sqare).find the times when the stone is at hight 62m above the ground.

If  s = 84t-5t^2,  solve 84t - 5t^2 = 62, a quadratic.

2.a stone is thrown vertically upward with an initial speed of 56m/s.its hight h metres above the ground after t sec is given by the formula 56t-5t2(square is on t).after how many sec will the stone be 50 m above the ground.

If h = 56t - 5t2, set 56t - 5t2 = 50, another quadratic.

3. a front wheels of a vehicle are 50 cm greater in circumference than the back wheels.the back wheels make 3 revolutions more than the front wheels in a distance of 15 m .find the circumference of the front wheels.

Let  C = the circumference of the back wheels in cm.
then C + 50 = the circumference of the front wheels.

then 1500/C = the number of revs on the back wheels,
and  1500/(C + 50) = the number of revs on the back wheels.

Now use your facts to write the equation:

the back wheels make 3 revolutions more than the front wheels


---------- FOLLOW-UP ----------

QUESTION: thanx a lot for answering my questions.you were a grt help.there are two more questions i would like to ask u.the questions are
1.a boat iscan travel at a speed of 12km/h in still water.if it takes 3 hours to go 15 km upstream and back,find the speed of current.
2.a cistern can be filled by two pipes.the small pipe alone will take 24 min longer than the large pipe to fill it alone.the small pipe alone will take take 32 mins longer to fill the cistern alone than when two pipes are operating togather.how long will it take the larger pipe to fill the cistern alone.

Answer
QUESTION: thanx a lot for answering my questions.you were a grt help.there are two more questions i would like to ask u.the questions are
1.a boat iscan travel at a speed of 12km/h in still water.if it takes 3 hours to go 15 km upstream and back,find the speed of current.

Start with:

Let  r = the speed of the current.  Now:

r - 12 = the speed of the boat upstream
r + 12 = the speed of the boat downstream

 15
------ = time needed to travel 15 km upstream
r - 12

 15
------ = time needed to travel 15 km downstream
r + 12

You can finish up.  It's the same as your No.3 above.

2. a cistern can be filled by two pipes.the small pipe alone will take 24 min longer than the large pipe to fill it alone.the small pipe alone will take take 32 mins longer to fill the cistern alone than when two pipes are operating togather.how long will it take the larger pipe to fill the cistern alone.

Let

L = rate of fill of larger pipe. (cisterns per minute)
S = rate of fill of smaller pipe.(cisterns per minute)

Then

1/L = time needed for larger pipe to fill.
1/S = time needed for smaler pipe to fill. << sorry
1/(L+S) = time needed for both pipes to fill.

and:

1/L = 1/S - 24          <<< LCD = LS
1/(L+S) = 1/S - 32      <<< LCD = S(L+S)

This one gets messy.  When I have more for you, I'll send a followup.