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5 years ago

a stone is thrown from the top of a cliff.

the height h in meters, of the stone above the ground level after t seconds is modeled by the function

h(t)=115+12.25t-4.9t^2.

a)give a physical interpretation of the meaning of the constant term 115 in the model.

b)write h(t) in the form A-B(t-C)^2, where A B and C are constant to be found.

c)using your answer to part b, or otherwise find with justification

i)the time taken after the stone is thrown for it to reach ground level.

ii)the maximum height of the stone above the ground and the time after which this

maximum height is reached

the height h in meters, of the stone above the ground level after t seconds is modeled by the function

h(t)=115+12.25t-4.9t^2.

a)give a physical interpretation of the meaning of the constant term 115 in the model.

b)write h(t) in the form A-B(t-C)^2, where A B and C are constant to be found.

c)using your answer to part b, or otherwise find with justification

i)the time taken after the stone is thrown for it to reach ground level.

ii)the maximum height of the stone above the ground and the time after which this

maximum height is reached

Reply 1

5 years ago

a) 115 is the height the stone is thrown from

b) dunno if right, but i got...

113.4375-4.9(t-5/4)^2

So A=113.4375, B=4.9, C=5/4

but doesn't work out for part c)i)

c)ii) maximum height above ground is the height the stone is dropped at? so 115? and time will be 0, since that's where the stone is dropped.

In general, I think the question is wrong...but I am not sure....Could you type out the whole question, pls?

b) dunno if right, but i got...

113.4375-4.9(t-5/4)^2

So A=113.4375, B=4.9, C=5/4

but doesn't work out for part c)i)

c)ii) maximum height above ground is the height the stone is dropped at? so 115? and time will be 0, since that's where the stone is dropped.

In general, I think the question is wrong...but I am not sure....Could you type out the whole question, pls?

Original post by neluxsan

a) 115 is the height the stone is thrown from

b) dunno if right, but i got...

113.4375-4.9(t-5/4)^2

So A=113.4375, B=4.9, C=5/4

but doesn't work out for part c)i)

c)ii) maximum height above ground is the height the stone is dropped at? so 115? and time will be 0, since that's where the stone is dropped.

In general, I think the question is wrong...but I am not sure....Could you type out the whole question, pls?

b) dunno if right, but i got...

113.4375-4.9(t-5/4)^2

So A=113.4375, B=4.9, C=5/4

but doesn't work out for part c)i)

c)ii) maximum height above ground is the height the stone is dropped at? so 115? and time will be 0, since that's where the stone is dropped.

In general, I think the question is wrong...but I am not sure....Could you type out the whole question, pls?

this is the whole question

Reply 3

5 years ago

sorry I suppose I don't know how to do it

Oh, I had a lot of fun doing this question the other day, I will try my best to explain it. I will spoiler block it incase someone wants to do it without the answers. Also, if you could tell me where you got this question from because im having trouble finding it now, and the work is in my folder at school...

Show spoiler Show spoiler Show spoiler Show spoiler

Reply 5

5 years ago

Where did you get the question from???? It came up in my mock exam.

Reply 6

4 years ago

Here are the answers:

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2^{ }- 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

Reply 7

3 years ago

Original post by systaniec324

Here are the answers:

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2 - 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2 - 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

thankyou

Original post by systaniec324

Here are the answers:

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2 - 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2 - 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

legend

Reply 10

2 weeks ago

Original post by systaniec324

Here are the answers:

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2^{ }- 2.5t)+155

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

9)

a) 115 m is the height of the cliff which means that's the stone's initial height as that's when t=0.

b) h(t) = -4.9(t^2

h(t) = -4.9(t - 1.25)^2 - (-4.9)(1.25)^2 +115

= -4.9(t - 1.25)^2 +122.65625

= 122.65625 - 4.9(t - 1.25)^2

c)

i) -4.9t^2 + 12.25t + 115 = 0 as the height is 0 when it's on the ground.

Find t using the completed square from part b or use the quadratic formula.

t=6.25 s , ignore any negative values as t can't be less than 0

ii) Using the completed square, we know that the max point of a curve is defined by the constant A. So max height of the stone is 123 m (3 s.f)

We also know that the constant C represents the time that the stone is in the air. Meaning time must be t=1.25 s.

tyvm

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